JEE Main 2016MathematicsApplication of DerivativesMediumMCQ

JEE Main 2016 — Application of Derivatives Question with Solution

JEE Main 2016 (09 Apr Online)

Question

If the tangent at a point P, with parameter t, on the curve x=4t2+3, y=8t3-1, t ∈R, meets the curve again at a point Q, then the coordinates of Q are :

Choose an option

Show full solutionCorrect option: D
Correct answer
Dt2+3, -t3-1

Step-by-step explanation

Given P4t2+3, 8t3-1

dydtdxdt=dydx=3t (slope of tangent at P)

Let Q=4λ2+3, 8λ3-1

Slope of PQ=3t

8t3-8λ34t2-4λ2=3t

⇒ t2+tλ-2λ2=0

t-λ t+2λ=0

t=λ  or  λ=-t2

∴ Qt2+3, -t3-1

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 2016, 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.