Explore Exams
Login Signup
Sign in Open App
Commerce Exam  >  Commerce Notes  >  Mathematics (Maths) Class 11  >  RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola

RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola

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
61 videos|222 docs|54 tests
Join Course for Free
About this Document
4.77/5 Rating
Mar 13, 2026 Last updated
Related Exams
Document Description: RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola for Commerce 2026 is part of Mathematics (Maths) Class 11 preparation. The notes and questions for RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola have been prepared according to the Commerce exam syllabus. Information about RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola covers topics like and RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola Example, for Commerce 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola.
Introduction of RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola in English is available as part of our Mathematics (Maths) Class 11 for Commerce & RD Sharma Solutions Commerce Maths Class 11 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 Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola
Description
Full syllabus notes, lecture & questions for RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola - Commerce | Plus exercises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 11 | Best notes, free PDF download
Information about RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola
In this doc you can find the meaning of RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola defined & explained in the simplest way possible. Besides explaining types of RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola theory, EduRev gives you an ample number of questions to practice RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola tests, examples and also practice Commerce tests
61 videos|222 docs|54 tests
Join Course for Free
Download as PDF
Explore Courses for Commerce exam
Related Searches
video lectures, Important questions, Summary, practice quizzes, MCQs, Viva Questions, mock tests for examination, RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola, Semester Notes, Exam, Sample Paper, study material, Extra Questions, Objective type Questions, shortcuts and tricks, Previous Year Questions with Solutions, Free, ppt, past year papers, RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola, pdf , RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola;
Additional Information about RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola for Commerce Preparation

RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola Free PDF Download

The RD Sharma Solutions Commerce Maths Class 11 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 Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola now and kickstart your journey towards success in the Commerce exam.

Importance of RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola

The importance of RD Sharma Solutions Commerce Maths Class 11 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 Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola Notes

RD Sharma Solutions Commerce Maths Class 11 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 Solutions Commerce Maths Class 11 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 Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola Notes on EduRev are your ultimate resource for success.

RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola Commerce Questions

The "RD Sharma Solutions Commerce Maths Class 11 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 Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola on the App

Students of Commerce can study RD Sharma Solutions Commerce Maths Class 11 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 Solutions Commerce Maths Class 11 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 Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Parabola is prepared as per the latest Commerce syllabus.
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup