JEE Main 2014MathematicsApplication of DerivativesMediumMCQ

JEE Main 2014 — Application of Derivatives Question with Solution

JEE Main 2014 (06 Apr)

Question

The slope of the line touching both the parabolas y2=4x and x2=-32y is 

Choose an option

Show full solutionCorrect option: C
Correct answer
C 1 2

Step-by-step explanation

y2=41x

x2=4-8y

The equation of the tangent to y2=4x is y= mx+am
The equation of the tangent to x2=4by is  y= mx-bm2

Since, they have a common tangent,

      am=-bm2

∴   1m=8m2

∴   m3=18

∴   m=12

∴  The slope of the common tangent is 1 2 .

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Application of Derivatives 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 2014, 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.