The length of the subtangent at $(2, 2)$ to the curve $x^5 = 2y^4$ is

The equation of the tangent to the curve $(\frac{x}{a})^n + (\frac{y}{b})^n = 2$ $(n \in N)$ at the point with abscissa equal to '$a$' is:

If $(a^2-1) x+a y+(3-a)=0$ is a normal to the curve $x y=1$,then the interval in which '$a$' lies is

What is the length of the normal at any point on the curve $y = \frac{1}{2}a(e^{x/a} + e^{-x/a})$?

If the tangent to the curve $y = \frac{x}{x^2-3}$,$x \in R, (x \neq \pm \sqrt{3})$ at a point $(\alpha, \beta) \neq (0,0)$ on it,is parallel to the line $2x + 6y - 11 = 0$,then

What is the angle between the curves $y = x^2$ and $x = y^2$ at the point $(1, 1)$?