JEE Main 2018MathematicsDifferential EquationsMediumMCQ

JEE Main 2018 — Differential Equations Question with Solution

JEE Main 2018 (16 Apr Online)

Question

The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, center at the origin and passing through the point 0,3 is

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Show full solutionCorrect option: A
Correct answer
Axyy'-y2+9=0

Step-by-step explanation

Let the equation of ellipse be x2a2+y2b2=1

It passes through 0,3⇒x2a2+y29=1  ...i 

Differentiating w.r.t. x,

⇒2xa2+2y9dydx=0

1a2=-y9xy'  ...ii

From i and ii we get,

-xy9y'+y29=1

⇒xyy'-y2+9=0

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About this question

This is a previous-year question from JEE Main 2018, covering the Differential Equations 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.