JEE Main 2018MathematicsApplication of DerivativesMediumMCQ

JEE Main 2018 — Application of Derivatives Question with Solution

JEE Main 2018 (08 Apr)

Question

If the curves y2=6x, 9x2+by2=16 intersect each other at right angles, then the value of b is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A92

Step-by-step explanation

Given, curves y2=6x and 9x2+by2=16
Let the point of intersection of curves be x1, y1. So,
2y1dydx=6
⇒  dydx=3y1
18x1+2by1dydx=0
⇒  dydx=-9x1by1

Since both the curve intersect at right angle.

3y1×-9x1by1=-1

⇒27x1=by12   (Since y12=6x1)

⇒27x1=b6x1

x1≠0

b=276=92

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About this question

This is a previous-year question from JEE Main 2018, covering the Application of Derivatives 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.