JEE Main 2014MathematicsEllipseMediumMCQ

JEE Main 2014 — Ellipse Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If OB is the semi-minor axis of an ellipse, F1 and F2 are its focii and the angle between F1B and F2B is a right angle, then the square of the eccentricity of the ellipse is

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Show full solutionCorrect option: C
Correct answer
C 1 2

Step-by-step explanation

In standard ellipse  x2a2+y2b2=1

Semi-major axis OA=a

Semi-minor axis OB=b

Focus F1≡-ae,0

F2≡ae,0



∠F1BF2=90°

OF1=OF2⇒∠F1BO=∠F2BO=45°

⇒aeb=tan45°=1 

⇒b=ae

Also, b2=a21-e2

⇒a2e2=a21-e2

⇒2e2=1

⇒e2=12

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About this question

This is a previous-year question from JEE Main 2014, 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.