Careers360 Logo
Engineering and Architecture
Search Colleges, Exams, Schools & more
JEE Main Eligibility Criteria 2025- Marks in 12th, Age Limit, Number of Attempts
  1. Home
  2. JEE Main
  3. Study Material
  4. Parametric equation of Ellipse - Practice Questions & MCQ

Parametric equation of Ellipse - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Parametric equation of Ellipse is considered one the most difficult concept.

  • 48 Questions around this concept.

Solve by difficulty

QuestionEASY

Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis.  If its eccentricity is \small \frac{3}{5}  and the distance between its foci is 6, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the end points of major and minor axes of ellipse, is

 

View Solution

The equation of the ellipse whose axes are the axes of coordinates and which passes through the point (–3, 1) and has eccentricity \sqrt{\frac{2}{5}}   is

View Solution

The equation of the circle passing through the foci of the ellipse \frac{x^{2}}{16}+\frac{y^{2}}{9}=1 , and having centre at

(0, 3) is :

View Solution

The foci of the ellipse \mathrm{25(x+1)^2+9(y+2)^2=225} are: 

View Solution

Concepts Covered - 1

Parametric equation of Ellipse

Parametric equation of Ellipse:

The equations x = a cosӨ, y = b sinӨ are called the parametric equation of the ellipse.

The circle described on the major axis as the diameter is called the auxiliary circle.

\\ {\text {Equation of Ellipse is } \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1} \\ {\text { Then, equation of auxiliary circle is } x^{2}+y^{2}=a^{2} \text { (As } A A^{\prime} \text { is Diameter) }}

Let P(x, y) be a point on the ellipse

Draw PN perpendicular to the major axis and PN to meet the auxiliary circle at Q. 

Let  \mathrm{\angle ACQ} be \theta (This angle is also known as Eccentric Angle). Hence, the parametric equation of circle at point Q (a cosӨ, a sinӨ).

Thus, P  has x-coordinate as a cosӨ

As P lies on the ellipse

\\ {\frac{\mathrm{a}^{2} \cos ^{2} \theta}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{b}^{2}}=1 \Rightarrow \mathrm{y}=\pm \mathrm{b} \sin \theta}\\ \\ {\text { Hence, Point } \mathrm{P} \text { is }(\mathrm{a} \cos \theta, \mathrm{b} \sin \theta)}

Study it with Videos

Parametric equation of Ellipse

Study other Related Concepts

Parametric equation of Ellipse Current Topic

Coordinate Axes
Distance Between Two Points Formula
Section Formula & Conic Sections
Centroid, Incentre and Circumcentre and Orthocentre of a Triangle
Excenters of Triangle
Circumcentre and Orthocentre
Incentre
Area of Triangle in Coordinate Geometry
Locus
Transformations of Axes

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Get Answer to all your questions

JEE Main Articles

JEE Main Syllabus 2025 PDF (Physics, Chemistry, Maths)
Oct 17, 2024
JEE Main Exam Date 2025 - NTA JEE Mains Session 1 & 2 Exam Schedule
Oct 17, 2024
JEE Main Registration 2025 Session 1, 2 - IIT Application Form Date, Fees, Documents Required
Oct 17, 2024
JEE Main Exam Pattern 2025 (Revised) - Total Marks in JEE Mains, Paper Pattern, Marking Scheme
Oct 17, 2024
JEE Main 2025 - Exam Pattern (Revised), Dates, Registration, Preparation Tips, Previous Year Papers
Oct 17, 2024
How to Prepare for JEE Main 2025?- Study Plan
Oct 17, 2024
JCECE Application Form 2024, Registration (Closed) - Apply Online here
Oct 17, 2024
JEE Main Login 2025 - Candidate Login for Registration, Result, Answer Key
Oct 16, 2024

B.Tech/B.Arch Admissions OPEN

UPES B.Tech Admissions 2025
UPES B.Tech Admissions 2025
Apply

Ranked #46 among universities in India by NIRF | Highest CTC 50 LPA | 100% Placements

Amity University, Noida B.Tech Admissions 2024
Amity University, Noida B.Tech Admissions 2024
Apply

Asia's Only University with the Highest US & UK Accreditation

JSS University Noida Admissions 2024
JSS University Noida Admissions 2024
Apply

170+ Recruiters Including Samsung, Zomato, LG, Adobe and many more | Highest CTC 47 LPA

Atlas SkillTech University | B.Tech Admissions
Atlas SkillTech University | B.Tech Admissions
Apply

Hands on Mentoring and Code Coaching | Cutting Edge Curriculum with Real World Application

Parul University B.Tech Admissions 2025
Parul University B.Tech Admissions 2025
Apply

India's youngest NAAC A++ accredited University | NIRF rank band 151-200 | 2200 Recruiters | 45.98 Lakhs Highest Package

Vidyashilp University B.Tech Admissions 2025
Vidyashilp University B.Tech Admissions 2025
Apply

Avail upto 100% Scholarships

View All Application Forms
News and Notifications
September 19, 2024 - 12:45 PM IST :
September 19, 2024 - 12:43 PM IST :
JEE Main 2025 Live: Exam date, registration soon; eligibility, syllabus, latest updates
October 18, 2024 - 07:53 AM IST
JEE Main 2025: NTA scraps optional questions in section B introduced during COVID pandemic
October 17, 2024 - 10:33 PM IST
How to prepare for JEE Main 2025 in 3 months? Study plan, important topics
October 17, 2024 - 05:18 PM IST
NTA Exam Calendar 2025 Live: JEE Main, NEET, CUET schedule to be announced soon; download at nta.ac.in
October 15, 2024 - 10:25 PM IST
NTA Exam Calendar 2025: JEE Main, NEET, CUET exam dates soon
October 15, 2024 - 07:24 AM IST
JEE Main, NEET, CUET 2025 Dates Live: NTA to announce exam calendar soon on nta.ac.in; latest updates
October 14, 2024 - 07:26 AM IST
NTA Exam Calendar 2025 Live: JEE Main, NEET, CUET, tentative schedule soon at nta.ac.in; how to download
October 12, 2024 - 09:40 PM IST

Download Careers360 App's

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

  • student
    300M+

    Students

  • colleges
    36,000+

    Colleges

  • exams
    550+

    Exams

  • ebook
    1500+

    E-Books

  • certification
    16000+

    Certifications

student
Mobile Screen

We Appeared in

Joint Entrance Examination (Main)      
JEE Main 2025 Sample Papers
Back to top