Length of Subnormal

Q. Find the length of subnormal at x= 2 on the curve y = $x^3$.

1. 96

Q.

In the figure, length of subnormal is the length P1N (tangent and normal is drawn at the point P)

1. T

Q. Find the length of subnormal at x= 2 on the curve y = $x^3$.

1. 96

Q. If ST and SN are the lengths of the subtangent and the subnormal at the point $\theta =\frac{\pi }{2}$ on the curve $x=a(\theta +sin\theta ),y=at(1-cos\theta ),a\ne 1,$ then
[Karnataka CET 2005]

1. ST = SN
2. ST = 2 SN
3. $S{T}^2=aS{N}^3$
4. $S{T}^3=aSN$