All Courses
Get the App Signup / Login
Sign in Open App
Commerce Exam  >  Commerce Notes  >  Mathematics (Maths) Class 11  >  RD Sharma Class 11 Solutions Chapter - Parabola

RD Sharma Class 11 Solutions Chapter - Parabola | Mathematics (Maths) Class 11 - Commerce PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


25. Parabola
Exercise 25.1
1 A. Question
Find the equation of the parabola whose:
focus is (3, 0) and the directrix is 3x + 4y = 1
Answer
Given that we need to find the equation of the parabola whose focus is S(3, 0) and directrix(M) is 3x + 4y - 1
= 0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 25x
2
 + 25y
2
 - 150x + 225 = 9x
2
 + 16y
2
 - 6x - 8y + 24xy + 1
? 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
?The equation of the parabola is 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
1 B. Question
Find the equation of the parabola whose:
focus is (1, 1) and the directrix is x + y + 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(1, 1) and directrix(M) is x + y + 1 =
0.
Page 2


25. Parabola
Exercise 25.1
1 A. Question
Find the equation of the parabola whose:
focus is (3, 0) and the directrix is 3x + 4y = 1
Answer
Given that we need to find the equation of the parabola whose focus is S(3, 0) and directrix(M) is 3x + 4y - 1
= 0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 25x
2
 + 25y
2
 - 150x + 225 = 9x
2
 + 16y
2
 - 6x - 8y + 24xy + 1
? 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
?The equation of the parabola is 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
1 B. Question
Find the equation of the parabola whose:
focus is (1, 1) and the directrix is x + y + 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(1, 1) and directrix(M) is x + y + 1 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 2x
2
 + 2y
2
 - 4x - 4y + 4 = x
2
 + y
2
 + 2x + 2y + 2xy + 1
? x
2
 + y
2
 + 2xy - 6x - 6y + 3 = 0
?The equation of the parabola is x
2
 + y
2
 + 2xy - 6x - 6y + 3 = 0.
1 C. Question
Find the equation of the parabola whose:
focus is (0, 0) and the directrix is 2x - y – 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(0, 0) and directrix(M) is 2x - y - 1 =
0.
Page 3


25. Parabola
Exercise 25.1
1 A. Question
Find the equation of the parabola whose:
focus is (3, 0) and the directrix is 3x + 4y = 1
Answer
Given that we need to find the equation of the parabola whose focus is S(3, 0) and directrix(M) is 3x + 4y - 1
= 0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 25x
2
 + 25y
2
 - 150x + 225 = 9x
2
 + 16y
2
 - 6x - 8y + 24xy + 1
? 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
?The equation of the parabola is 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
1 B. Question
Find the equation of the parabola whose:
focus is (1, 1) and the directrix is x + y + 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(1, 1) and directrix(M) is x + y + 1 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 2x
2
 + 2y
2
 - 4x - 4y + 4 = x
2
 + y
2
 + 2x + 2y + 2xy + 1
? x
2
 + y
2
 + 2xy - 6x - 6y + 3 = 0
?The equation of the parabola is x
2
 + y
2
 + 2xy - 6x - 6y + 3 = 0.
1 C. Question
Find the equation of the parabola whose:
focus is (0, 0) and the directrix is 2x - y – 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(0, 0) and directrix(M) is 2x - y - 1 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 5x
2
 + 5y
2
 = 4x
2
 + y
2
 - 4x + 2y - 4xy + 1
? x
2
 + 4y
2
 + 4xy + 4x - 2y - 1 = 0
?The equation of the parabola is x
2
 + 4y
2
 + 4xy + 4x - 2y - 1 = 0.
1 D. Question
Find the equation of the parabola whose:
focus is (2, 3) and the directrix is x - 4y + 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(2, 3) and directrix(M) is x - 4y + 3 =
0.
Page 4


25. Parabola
Exercise 25.1
1 A. Question
Find the equation of the parabola whose:
focus is (3, 0) and the directrix is 3x + 4y = 1
Answer
Given that we need to find the equation of the parabola whose focus is S(3, 0) and directrix(M) is 3x + 4y - 1
= 0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 25x
2
 + 25y
2
 - 150x + 225 = 9x
2
 + 16y
2
 - 6x - 8y + 24xy + 1
? 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
?The equation of the parabola is 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
1 B. Question
Find the equation of the parabola whose:
focus is (1, 1) and the directrix is x + y + 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(1, 1) and directrix(M) is x + y + 1 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 2x
2
 + 2y
2
 - 4x - 4y + 4 = x
2
 + y
2
 + 2x + 2y + 2xy + 1
? x
2
 + y
2
 + 2xy - 6x - 6y + 3 = 0
?The equation of the parabola is x
2
 + y
2
 + 2xy - 6x - 6y + 3 = 0.
1 C. Question
Find the equation of the parabola whose:
focus is (0, 0) and the directrix is 2x - y – 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(0, 0) and directrix(M) is 2x - y - 1 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 5x
2
 + 5y
2
 = 4x
2
 + y
2
 - 4x + 2y - 4xy + 1
? x
2
 + 4y
2
 + 4xy + 4x - 2y - 1 = 0
?The equation of the parabola is x
2
 + 4y
2
 + 4xy + 4x - 2y - 1 = 0.
1 D. Question
Find the equation of the parabola whose:
focus is (2, 3) and the directrix is x - 4y + 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(2, 3) and directrix(M) is x - 4y + 3 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 17x
2
 + 17y
2
 - 68x - 102y + 221 = x
2
 + 16y
2
 + 6x - 24y - 8xy + 9
? 16x
2
 + y
2
 + 8xy - 74x - 78y + 212 = 0
?The equation of the parabola is 16x
2
 + y
2
 + 8xy - 74x - 78y + 212 = 0.
2. Question
Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0. Also,
find the length of its latus - rectum.
Answer
Given that we need to find the equation of the parabola whose focus is S(2, 3) and directrix(M) is x - 4y + 3 =
0.
Page 5


25. Parabola
Exercise 25.1
1 A. Question
Find the equation of the parabola whose:
focus is (3, 0) and the directrix is 3x + 4y = 1
Answer
Given that we need to find the equation of the parabola whose focus is S(3, 0) and directrix(M) is 3x + 4y - 1
= 0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 25x
2
 + 25y
2
 - 150x + 225 = 9x
2
 + 16y
2
 - 6x - 8y + 24xy + 1
? 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
?The equation of the parabola is 16x
2
 + 9y
2
 - 24xy - 144x + 8y + 224 = 0
1 B. Question
Find the equation of the parabola whose:
focus is (1, 1) and the directrix is x + y + 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(1, 1) and directrix(M) is x + y + 1 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 2x
2
 + 2y
2
 - 4x - 4y + 4 = x
2
 + y
2
 + 2x + 2y + 2xy + 1
? x
2
 + y
2
 + 2xy - 6x - 6y + 3 = 0
?The equation of the parabola is x
2
 + y
2
 + 2xy - 6x - 6y + 3 = 0.
1 C. Question
Find the equation of the parabola whose:
focus is (0, 0) and the directrix is 2x - y – 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(0, 0) and directrix(M) is 2x - y - 1 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 5x
2
 + 5y
2
 = 4x
2
 + y
2
 - 4x + 2y - 4xy + 1
? x
2
 + 4y
2
 + 4xy + 4x - 2y - 1 = 0
?The equation of the parabola is x
2
 + 4y
2
 + 4xy + 4x - 2y - 1 = 0.
1 D. Question
Find the equation of the parabola whose:
focus is (2, 3) and the directrix is x - 4y + 1 = 0
Answer
Given that we need to find the equation of the parabola whose focus is S(2, 3) and directrix(M) is x - 4y + 3 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 17x
2
 + 17y
2
 - 68x - 102y + 221 = x
2
 + 16y
2
 + 6x - 24y - 8xy + 9
? 16x
2
 + y
2
 + 8xy - 74x - 78y + 212 = 0
?The equation of the parabola is 16x
2
 + y
2
 + 8xy - 74x - 78y + 212 = 0.
2. Question
Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x – 4y + 3 = 0. Also,
find the length of its latus - rectum.
Answer
Given that we need to find the equation of the parabola whose focus is S(2, 3) and directrix(M) is x - 4y + 3 =
0.
Let us assume P(x, y) be any point on the parabola.
We know that the point on the parabola is equidistant from focus and directrix.
We know that the distance between two points (x
1
, y
1
) and (x
2
, y
2
) is .
We know that the perpendicular distance from a point (x
1
, y
1
) to the line ax + by + c = 0 is .
? SP = PM
? SP
2
 = PM
2
? 
? 
? 
? 17x
2
 + 17y
2
 - 68x - 102y + 221 = x
2
 + 16y
2
 + 6x - 24y - 8xy + 9
? 16x
2
 + y
2
 + 8xy - 74x - 78y + 212 = 0
?The equation of the parabola is 16x
2
 + y
2
 + 8xy - 74x - 78y + 212 = 0.
We know that the length of the latus rectum is twice the perpendicular distance from the focus to the
directrix.
? 
? 
? 
?The length of the latus rectum is .
3 A. Question
Find the equation of the parabola, if
the focus is at (- 6, 6) and the vertex is at (- 2, 2)
Answer
We need to find the equation of the parabola whose focus is (- 6, 6), and the vertex is (- 2, 2).
Read More
75 videos|238 docs|91 tests
Join Course for Free

Top Courses for Commerce

Related Exams
About this Document
Oct 24, 2024 Last updated
Document Description: RD Sharma Class 11 Solutions Chapter - Parabola for Commerce 2024 is part of Mathematics (Maths) Class 11 preparation. The notes and questions for RD Sharma Class 11 Solutions Chapter - Parabola have been prepared according to the Commerce exam syllabus. Information about RD Sharma Class 11 Solutions Chapter - Parabola covers topics like and RD Sharma Class 11 Solutions Chapter - Parabola Example, for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Class 11 Solutions Chapter - Parabola.
Introduction of RD Sharma Class 11 Solutions Chapter - Parabola in English is available as part of our Mathematics (Maths) Class 11 for Commerce & RD Sharma Class 11 Solutions Chapter - Parabola in Hindi for Mathematics (Maths) Class 11 course. Download more important topics related with notes, lectures and mock test series for Commerce Exam by signing up for free. Commerce: RD Sharma Class 11 Solutions Chapter - Parabola | Mathematics (Maths) Class 11 - Commerce
Description
Full syllabus notes, lecture & questions for RD Sharma Class 11 Solutions Chapter - Parabola | Mathematics (Maths) Class 11 - Commerce - Commerce | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 11 | Best notes, free PDF download
Information about RD Sharma Class 11 Solutions Chapter - Parabola
In this doc you can find the meaning of RD Sharma Class 11 Solutions Chapter - Parabola defined & explained in the simplest way possible. Besides explaining types of RD Sharma Class 11 Solutions Chapter - Parabola theory, EduRev gives you an ample number of questions to practice RD Sharma Class 11 Solutions Chapter - Parabola tests, examples and also practice Commerce tests
75 videos|238 docs|91 tests
Join Course for Free
Download as PDF
Explore Courses for Commerce exam

Top Courses for Commerce

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Viva Questions

,

practice quizzes

,

pdf

,

Previous Year Questions with Solutions

,

ppt

,

RD Sharma Class 11 Solutions Chapter - Parabola | Mathematics (Maths) Class 11 - Commerce

,

MCQs

,

RD Sharma Class 11 Solutions Chapter - Parabola | Mathematics (Maths) Class 11 - Commerce

,

Summary

,

past year papers

,

Free

,

Objective type Questions

,

RD Sharma Class 11 Solutions Chapter - Parabola | Mathematics (Maths) Class 11 - Commerce

,

video lectures

,

Sample Paper

,

study material

,

Semester Notes

,

Important questions

,

Extra Questions

,

shortcuts and tricks

,

mock tests for examination

,

Exam

;
Additional Information about RD Sharma Class 11 Solutions Chapter - Parabola for Commerce Preparation

RD Sharma Class 11 Solutions Chapter - Parabola Free PDF Download

The RD Sharma Class 11 Solutions Chapter - Parabola is an invaluable resource that delves deep into the core of the Commerce exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the RD Sharma Class 11 Solutions Chapter - Parabola now and kickstart your journey towards success in the Commerce exam.

Importance of RD Sharma Class 11 Solutions Chapter - Parabola

The importance of RD Sharma Class 11 Solutions Chapter - Parabola cannot be overstated, especially for Commerce aspirants. This document holds the key to success in the Commerce exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

RD Sharma Class 11 Solutions Chapter - Parabola Notes

RD Sharma Class 11 Solutions Chapter - Parabola Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RD Sharma Class 11 Solutions Chapter - Parabola. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, RD Sharma Class 11 Solutions Chapter - Parabola Notes on EduRev are your ultimate resource for success.

RD Sharma Class 11 Solutions Chapter - Parabola Commerce Questions

The "RD Sharma Class 11 Solutions Chapter - Parabola Commerce Questions" guide is a valuable resource for all aspiring students preparing for the Commerce exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study RD Sharma Class 11 Solutions Chapter - Parabola on the App

Students of Commerce can study RD Sharma Class 11 Solutions Chapter - Parabola alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Class 11 Solutions Chapter - Parabola, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of RD Sharma Class 11 Solutions Chapter - Parabola is prepared as per the latest Commerce syllabus.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up
within 7 days!
Takes less than 10 seconds to signup