JEE Main 2016 — Application Of Derivatives Question with Solution
From: JEE Main 2016 (Online) 9th April Morning Slot
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: A
Correct answer
A(t2 + 3, − t3 −1)
Step-by-step explanation
Given, x = 4t2 + 3 and y = 8t3 1
P (4t2 + 3, 8t3 1)
and 24t2
Slope of tangent at
P 3t
Assume Q (42 + 3, 83 1)
Slope of PQ 3t
22 + 2t2 + 2t 3t (t + )
t2 + t 22 = 0
(t ) (t + 2) 0
t or
Q (4t2 + 3, 8t3 1) Or
Q
(t2 + 3, t3 1)
P (4t2 + 3, 8t3 1)
and 24t2
Slope of tangent at
P 3t
Assume Q (42 + 3, 83 1)
Slope of PQ 3t
22 + 2t2 + 2t 3t (t + )
t2 + t 22 = 0
(t ) (t + 2) 0
t or
Q (4t2 + 3, 8t3 1) Or
Q
(t2 + 3, t3 1)
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