JEE Main 2017MathematicsEllipseMediumMCQ

JEE Main 2017 — Ellipse Question with Solution

JEE Main 2017 (09 Apr Online)

Question

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points 4,-1 and -2,2 is

Choose an option

Show full solutionCorrect option: A
Correct answer
A32

Step-by-step explanation

Equation of ellipse whose centre at 0,0 is

x2a2+y2b2=1

It passes through (4,−1)

⇒16a2+1b2=1

⇒16b2+a2=a2b2 ...i

Again it passes through (−2,2)

⇒4a2+4b2=1

⇒4b2+4a2=a2b2 ...ii

From the equation i and ii, we get, 

16b2+a2=4a2+4b2

⇒a2=4b2

  Now, we have, e2=1-b2a2=1-14=34

⇒e=32.

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About this question

This is a previous-year question from JEE Main 2017, covering the Ellipse chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.