Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Find the lengths of tangent, subtangent, normal and
subnormal to y 2 = 4ax at (at 2 , 2at) -
A
2at 
, 2a 
, 2at 2 , 2a
, 2a , 2at 2 , 2a
B
2a 
, 2at 2 , 2a, 2at 
, 2at 2 , 2a, 2at
C
2 
, 2at 
, 2a, 2a t 2
, 2at , 2a, 2a t 2
D
None of these
Text Solution
Verified by ExpertsThe correct answer is:
A
We have the given curve,
y 2 = 4ax … (i)
Differentiating equation (i) both sides w.r.t. x, we get
2y 
= 4a
= 
= 
… (ii)
Now, the length of tangent at (at 2 , 2at) is
= 
⇒ = 2at 
[using (ii)]
∴ Length of normal at (at 2 , 2at) is
⇒ = 
⇒ = 2at 
⇒ = 2a 
∴ Length of subtangent ⇒ 
= 
= 2at 2
Length of subnormal ⇒ y 1 
= 2at . 
= 2a.
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