Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The number of distinct line(s) which is/are tangent at a point on curve 4x 3 = 27 y 2 and normal at other point, is :
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Parametric form of curve is x = 3t 2 , y = 2t 3
= t
Let P 
, Q 
Conditions are
(i) 
= – 1
(ii) 
= Slope of line segment PQ
t 1 t 2 = – 1 ...(i) ; t 1 = 
...(ii)
⇒ 3( – 1 + t 12 ) = 2 
t 12 = 
+ 1
t 12 = 2, – 1
t 12 = 2 ⇒ t 1 = ± 
⇒ t 2 = 
If t 1 = 
, t 2 = – 
⇒ P(6, 4 
), Q 
⇒ Required line is y = 
x – 2 
If t 1 = – 
, t 2 = 
⇒ P(6, – 4 
), Q 
⇒ Required line is y = – 
x + 2 
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