JEE Main 2017MathematicsDifferential EquationsMediumMCQ

JEE Main 2017 — Differential Equations Question with Solution

JEE Main 2017 (09 Apr Online)

Question

A tangent to the curve, y=fx at Px, y meets x-axis at A and y-axis at B. If AP:BP=1:3 and f1=1, then the curve also passes through the point

Choose an option

Show full solutionCorrect option: C
Correct answer
C2,18

Step-by-step explanation

Equation of tangent,

Y−y= dy dx (X−x) A( x−y dx dy ,0 )  ​:  B( 0,y−x dy dx )

Given, AP:BP=1:3,

Using section formula, we get

y=y−xdydx4

⇒y−xdydx=4y

⇒dyy+3dxx=0

By integrating w.r.t x, we get

ln|y|+3ln|x|=lnc

|yx3|=c

∵f(1)=1

∴c=1

⇒|yx3|=1

Hence, the curve passes throught the point 2,18

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About this question

This is a previous-year question from JEE Main 2017, 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.