Andhra Pradesh Board Solutions for Chapter: Applications of Derivatives, Exercise 3: Exercise 10(c)

Find the length of sub-tangent and sub normal at a point of the curve $y=b·\sin \frac{x}{a}$,

Show that the length of sub-normal at any point on the curve $xy=a^2$ varies as the cube of the ordinate of the point.

Show that at any point $(x, y)$ on the curve $y=b{e}^{\frac{x}{a}}$, the length of the sub-
tangent is constant and the length of the sub-normal is $\frac{y^2}{a}$.

Find the value of $k$ so that the length of the sub-normal at any point on the curve $x·y^k=a^{k+1}$ is constant.

At any point $t$ on the curve $x=a(t+\sin t), y=a(1-\cos t)$. Find the lengths of the tangent, normal, sub-tangent and sub-normal.

Find the length of normal and sub-normal at a point on the curve $y=\frac{a}{2}\left(e^{\frac{x}{a}}+e^{\frac{-x}{a}}\right)$

Find the length of the sub-tangent and sub-normal of a point $t$ on the curve $x=a(\cos t+t\sin t), y=a(\sin t-t\cos t)$