JEE Main 2020MathematicsEllipseMediumMCQ

JEE Main 2020 — Ellipse Question with Solution

JEE Main 2020 (09 Jan Shift 2)

Question

The length of the minor axis (along y-axis) of an ellipse in the standard form is 43. If this ellipse touches the line x+6y=8 then its eccentricity is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A12113

Step-by-step explanation

Let equation of ellipse be x2a2+y2b2=1.

Here, 2b=43⇒b=23

Equation of tangents ≡y=mx±a2m2+b2

Comparing with ≡y=-x6+43

m=-16 and a2m2+b2=169

⇒a236+43=169

⇒a236=169-43=49

⇒a2=16

Now, e=1-b2a2

⇒e=1-43×16=1112

⇒e=12113

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Ellipse chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2020, 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.