Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Coordinates of the point P on the curve y 2 = 2x 3 the tangent at which is perpendicular to the line 4x – 3y + 2 = 0 are given by
A
(2, 4)
B
(0, 0)
C
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
C
y 2 = 2x 3 2y 
= 6x
2 ⇒ 
= 
tangent is ⊥ to 4x – 3y + 2 = 0
⇒ slope of this line = 4/3
both are ⊥ ∴ 
× 
= –1 ⇒ 4x 2 = –y
solving y 2 = 2x 3 and 4x 2 = –y
we get x = 0 or x = 1/8
when x = 0 we get y = 0, but at (0, 0) slope of tangent 
from (i) does not exist
∴ (0, 0) does not lie on the curve
Now when x = 
, y = – 
. Point 
lies on the curve also. So it is the required point.
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