NCERT Solutions for Miscellaneous Exercise Chapter 11 Class 11 - Conic Section

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# NCERT Solutions for Miscellaneous Exercise Chapter 11 Class 11 - Conic Section

Edited By Vishal kumar | Updated on Nov 20, 2023 11:49 AM IST

## NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Miscellaneous Exercise- Download Free PDF

NCERT Solutions for Class 11 Maths Chapter 11: Conic Sections Miscellaneous Exercise- In the previous exercises of this chapter, you have already learned about the conic sections such as circle, parabola, hyperbola, and ellipse. In the NCERT solutions for Class 11 Maths chapter 11 miscellaneous exercise, you will get mixed concepts questions from all the topics of the conic sections. Miscellaneous exercise Chapter 11 Class 11 is considered to be tougher than all the previous exercises of this chapter. It will check your conceptual understanding of this chapter.

If you are done with the other exercises of this chapter, you start solving problems from miscellaneous exercise chapter 11 Class 11. You will find difficulties while solving these problems at first but Class 11 Maths chapter 11 miscellaneous solutions are here to help you. These NCERT solutions are designed in a detailed manner that could be understood by an average student also. There are very few questions in the CBSE Exam that are asked for the miscellaneous exercise, but miscellaneous exercises are very important for the engineering competitive exams like JEE Main, SRMJEE, etc. You must solve the miscellaneous exercises if you are preparing for any engineering entrance exams. The class 11 chapter 11 maths miscellaneous solutions are written by subject experts from Careers360, presented in easily understandable language with detailed explanations. Also, the class 11 maths ch 11 miscellaneous exercise solutions are available in a downloadable PDF format, allowing students to access and use them anytime, free of charge. This resource is designed to enhance students' understanding and facilitate convenient and cost-free self-study. If you are looking for NCERT solutions for other classes, click on the NCERT Solutions link.

Also, see

**In the CBSE Syllabus for 2023-24, this miscellaneous exercise class 11 chapter 11 has been renumbered as Chapter 10.

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## Access Conic Section Class 11 Chapter 11 Miscellaneous Exercise

Answer:

Le the parabolic reflector opens towards the right.

So the equation of parabolic reflector will be,

$y^2=4ax$

Now, Since this curve will pass through the point (5,10) if we assume origin at the optical centre,

So

$10^2=4a(5)$

$a=\frac{100}{20}=5$

Hence, The focus of the parabola is,

$(a,0)=(5,0)$.

Alternative Method,

As we know on any concave curve

$f=\frac{R}{2}$

Hence, Focus

$f=\frac{R}{2}=\frac{10}{2}=5$.

Hence the focus is 5 cm right to the optical centre.

Answer:

Since the Axis of the parabola is vertical, Let the equation of the parabola be,

$x^2=4ay$

it can be seen that this curve will pass through the point (5/2, 10) if we assume origin at the bottom end of the parabolic arch.

So,

$\left(\frac{5}{2}\right)^2=4a(10)$

$a=\frac{25}{160}=\frac{5}{32}$

Hence, the equation of the parabola is

$x^2=4\times\frac{5}{32}\times y$

$x^2=\frac{20}{32} y$

$x^2=\frac{5}{8} y$

Now, when y = 2 the value of x will be

$x=\sqrt{(\frac{5}{8}\times2)}=\sqrt{\frac{5}{4}}=\frac{\sqrt{5}}{2}$

Hence the width of the arch at this height is

$2x=2\times\frac{\sqrt{5}}{2}=\sqrt{5}.$

Answer:

Given,

The width of the parabolic cable = 100m

The length of the shorter supportive wire attached = 6m

The length of the longer supportive wire attached = 30m

Since the rope opens towards upwards, the equation will be of the form

$x^2=4ay$

Now if we consider origin at the centre of the rope, the equation of the curve will pass through points, (50,30-6)=(50,24)

$24^2=4a50$

$a=\frac{625}{24}$

Hence the equation of the parabola is

$x^2=4\times \frac{625}{24}\times y$

$x^2= \frac{625}{6}\times y$

Now at a point, 18 m right from the centre of the rope, the x coordinate of that point will be 18, so by the equation, the y-coordinate will be

$y=\frac{x^2}{4a}=\frac{18^2}{4\times \frac{625}{6}}\approx 3.11m$

Hence the length of the supporting wire attached to roadway from the middle is 3.11+6=9.11m.

Answer:

The equation of the semi-ellipse will be of the form

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\:,y>0$

Now, According to the question,

the length of major axis = 2a = 8 $\Rightarrow a=4$

The length of the semimajor axis =2$\Rightarrow b=2$

Hence the equation will be,

$\frac{x^2}{4^2}+\frac{y^2}{2^2}=1\:,y>0$

$\frac{x^2}{16}+\frac{y^2}{4}=1\:,y>0$

Now, at point 1.5 cm from the end, the x coordinate is 4-1.5 = 2.5

So, the height at this point is

$\frac{(2.5)^2}{16}+\frac{y^2}{4}=1\Rightarrow y=\sqrt{4(1-\frac{2.5^2}{16})}$

$y\approx 1.56m$

Hence the height of the required point is 1.56 m.

Answer:

Let $\theta$ be the angle that rod makes with the ground,

Now, at a point 3 cm from the end,

$\cos\theta=\frac{x}{9}$

At the point touching the ground

$\sin\theta=\frac{y}{3}$

Now, As we know the trigonometric identity,

$\sin^2\theta+\cos^2\theta=1$

$\left (\frac{x}{9} \right )^2+\left ( \frac{y}{3} \right )^2=1$

$\frac{x^2}{81}+\frac{y^2}{9}=1$

Hence the equation is,

$\frac{x^2}{81}+\frac{y^2}{9}=1$

Answer:

Given the parabola,

$x^2=12y$

Comparing this equation with $x^2=4ay$, we get

$a=3$

Now, As we know the coordinates of ends of latus rectum are:

$(2a,a)\:and\:(-2a,a)$

So, the coordinates of latus rectum are,

$(2a,a)\:and\:(-2a,a)=(6,3)\:and\:(-6,3)$

Now the area of the triangle with coordinates (0,0),(6,3) and (-6,3)

Widht of the triangle = 2*6=12

Height of the triangle = 3

So The area =

$\frac{1}{2}\times base\times height=\frac{1}{2}\times12\times3=18$

Hence the required area is 18 unit square.

Answer:

As we know that if a point moves in a plane in such a way that its distance from two-point remain constant then the path is an ellipse.

Now, According to the question,

the distance between the point from where the sum of the distance from a point is constant = 10

$\Rightarrow 2a=10\Rightarrow a=5$

Now, the distance between the foci=8

$\Rightarrow 2c=8\Rightarrow c=4$

Now, As we know the relation,

$c^2=a^2-b^2$

$b^2=a^2-c^2$

$b=\sqrt{a^2-c^2}=\sqrt{5^2-4^2}=\sqrt{25-16}=\sqrt{9}=3$

Hence the equation of the ellipse is,

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$\Rightarrow \frac{x^2}{5^2}+\frac{y^2}{3^2}=1$

$\Rightarrow \frac{x^2}{25}+\frac{y^2}{9}=1$

Hence the path of the man will be

$\Rightarrow \frac{x^2}{25}+\frac{y^2}{9}=1$

Answer:

Given, an equilateral triangle inscribed in parabola with the equation.$y^2 = 4 ax$

The one coordinate of the triangle is A(0,0).

Now, let the other two coordinates of the triangle are

$B(x,\sqrt{4ax})$ and $C(x,-\sqrt{4ax})$

Now, Since the triangle is equilateral,

$BC=AB=CA$

$2\sqrt{4ax}=\sqrt{(x-0)^2+(\sqrt{4ax}-0)^2}$

$x^2=12ax$

$x=12a$

The coordinates of the points of the equilateral triangle are,

$(0,0),(12,\sqrt{4a\times 12a}),(12,-\sqrt{4a\times 12a})=(0,0),(12,4\sqrt{3}a)\:and\:(12,-4\sqrt{3}a)$

So, the side of the triangle is

$2\sqrt{4ax}=2\times4\sqrt{3}a=8\sqrt{3}a$

## More About NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercise:-

As the name suggests miscellaneous exercise chapter 11 Class 11 consists of a mixture of questions from all the topics covered in this chapter. Most of the questions in the miscellaneous exercise chapter 11 Class 11 are related to real-life applications of conic sections such as circle, parabola, ellipse and hyperbola. There are few examples given before this exercise that you can solve.

## Topic Covered in Class 11 Maths ch 11 Miscellaneous Exercise Solutions

The Miscellaneous Exercise in NCERT Solutions for Class 11 Maths Chapter 11 - Conic Sections is centred around the following topics:

1. Sections of a Cone
2. Circle
3. Parabola
4. Ellipse
5. Hyperbola
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Each question in the class 11 chapter 11 miscellaneous exercise has been meticulously solved to aid students in understanding the concepts, with an eye on the examination. The NCERT Solutions for Class 11 Maths play a crucial role in providing in-depth comprehension of all the concepts covered in Class 11 Mathematics.

Also Read| Conic Section Class 11 Notes

## Benefits of NCERT Solutions for Class 11 Maths Chapter 11 Miscellaneous Exercise:-

• Class 11 Maths chapter 11 miscellaneous exercise solutions are explained in a detailed manner by experts who knows how to answer the in the CBSE exam.
• You can use NCERT solutions for Class 11 Maths chapter 11 miscellaneous exercise for reference while solving them.

## Key Features of Class 11 Chapter 11 Maths Miscellaneous Solutions

Key features of Class 11 Maths Chapter 11 Miscellaneous Exercise Solutions on Conic Sections include:

1. Comprehensive Coverage: Miscellaneous exercise class 11 chapter 11 solution covers all the miscellaneous exercises in Chapter 11, addressing key topics related to Conic Sections.

2. Careful Problem Solving: Each class 11 maths miscellaneous exercise chapter 11 question is carefully solved, ensuring clarity and understanding for students.

3. Exam-Oriented Approach: Class 11 maths ch 11 miscellaneous exercise solutions are crafted with the examination in mind, providing students with a strategic approach to problem-solving.

4. Variety of Problems: A diverse range of problems is included in the miscellaneous exercise, catering to different difficulty levels and scenarios.

5. Accessible Language: Class 11 chapter 11 miscellaneous exercise solutions are presented in clear and concise language, making complex geometric concepts associated with Conic Sections more accessible for students.

6. PDF Version Access: The solutions are available in a downloadable PDF format, offering students convenient offline access for study.

## Subject Wise NCERT Exampler Solutions

Happy learning!!!

### Frequently Asked Question (FAQs)

1. Write the equation of a circle with centre (1,2) and the radius 5 ?

Equation of circle => (x-1)^2 + (y-2)^2 = 5^2

x^2 -2x + 1 + y^2 + 4y + 4 = 25

x^2 -2x + y^2 + 4y = 20

2. Write the equation of the parabola with focus at (2, 0) and directrix x = – 2 ?

Equation of the parabola =>  y^2 = 4(2)x

y^2 = 8x

3. Find the coordinates of the focus of the parabola y^2 = 12x

Given equation of the parabola  => y^2  = 12x

Compare with y^2 = 4ax   =>  a = 3

Coordinate of focus is (3,0).

4. Find the axis of the parabola y^2 = 12x

The given equation involves y^2, so the axis of symmetry is along the x-axis. The axis of the parabola is the x-axis.

5. Find the equation of the directrix of the parabola y^2 = 12x

Given equation of the parabola  => y^2  = 12x

Compare with y^2 = 4ax   =>  a = 3

The equation of the directrix of the parabola is x = – 3

6. Find the the length of the latus rectum of the parabola y^2 = 12x

Given equation of the parabola  => y^2  = 12x

Compare with y^2 = 4ax   =>  a = 3

Length of the latus rectum is 4a = 4 × 3 = 12.

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An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

2 Jobs Available
##### Fashion Blogger

Fashion bloggers use multiple social media platforms to recommend or share ideas related to fashion. A fashion blogger is a person who writes about fashion, publishes pictures of outfits, jewellery, accessories. Fashion blogger works as a model, journalist, and a stylist in the fashion industry. In current fashion times, these bloggers have crossed into becoming a star in fashion magazines, commercials, or campaigns.

2 Jobs Available
##### Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.

3 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
##### Advertising Manager

Advertising managers consult with the financial department to plan a marketing strategy schedule and cost estimates. We often see advertisements that attract us a lot, not every advertisement is just to promote a business but some of them provide a social message as well. There was an advertisement for a washing machine brand that implies a story that even a man can do household activities. And of course, how could we even forget those jingles which we often sing while working?

2 Jobs Available
##### Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
##### Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
##### Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

5 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Procurement Manager

The procurement Manager is also known as  Purchasing Manager. The role of the Procurement Manager is to source products and services for a company. A Procurement Manager is involved in developing a purchasing strategy, including the company's budget and the supplies as well as the vendors who can provide goods and services to the company. His or her ultimate goal is to bring the right products or services at the right time with cost-effectiveness.

2 Jobs Available
##### Process Development Engineer

The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.

2 Jobs Available
##### AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.

4 Jobs Available
##### Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.

4 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### .NET Developer

.NET Developer Job Description: A .NET Developer is a professional responsible for producing code using .NET languages. He or she is a software developer who uses the .NET technologies platform to create various applications. Dot NET Developer job comes with the responsibility of  creating, designing and developing applications using .NET languages such as VB and C#.

2 Jobs Available
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