JEE Main 2021MathematicsApplication Of DerivativesTangent And NormalmediumMCQ
JEE Main 2021 — Application Of Derivatives Question with Solution
From: JEE Main 2021 (Online) 24th February Morning Shift
Question
If the tangent to the curve y = x3 at the point P(t, t3) meets the curve again at Q, then the
ordinate of the point which divides PQ internally in the ratio 1 : 2 is :
Choose an option
▸Show full solutionCorrect option: C
Correct answer
C-2t3
Step-by-step explanation
Given P(t,t3)
Let Q=(t1,t13)
Slope of tangent at point p,
dxdy=3x2
⇒dxdy(t,t3)=3t2
This slope is same as slope of line PQ.
Slope of PQ=t1−tt13−t3
∴3t2=t1−tt13−t3
⇒3t2=(t1−t)(t1−t)(t12+tt1+t2)
⇒3t2=t12+tt1+t2
⇒t1=−2t
∴Q=(−2t,−8t3)
∴h=32t−2t=0
k=32t3−8t3=−2t3
∴ Point M=(0,−2t3)
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.
This is a previous-year question from JEE Main 2021, 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.
