JEE Main 2014MathematicsDifferential EquationsMediumMCQ

JEE Main 2014 — Differential Equations Question with Solution

JEE Main 2014 (09 Apr Online)

Question

If the differential equation representing the family of all circles touching x-axis at the origin is x2-y2dydx=gxy, then gx equals

Choose an option

Show full solutionCorrect option: B
Correct answer
B2x

Step-by-step explanation

Equation of circle touching x-axis in origin is x-02+y-k2=k2
⇒x2+y2-2ky=0   ...1, where k is the radius of the circle.

Differentiating the above equation w.r.t. x, we get, 

2x+2ydydx-2kdydx=0

⇒x+y-kdydx=0

From equation 1,

⇒x+y-x2+y22ydydx=0

⇒x2-y2dydx=2xy=gxy

⇒gx=2x

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About this question

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