The length of the normal at any point to the curve $y=c \cosh \left(\frac{x}{c}\right)$ is

What is the angle between the curves $y = x^2$ and $6y = 7 - x^3$ at the point $(1, 1)$?

The abscissa of the point on the curve $y=a\left(e^{\frac{x}{a}}+e^{-\frac{x}{a}}\right)$ where the tangent is parallel to the $X$-axis is

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

If the tangent and the normal drawn to the curve $xy^2 + x^2y = 12$ at the point $(1, 3)$ meet the $X$-axis in $T$ and $N$ respectively, then $TN =$

The sum of the intercepts on the axes cut off by the tangent to the curve $x^{2/3} + y^{2/3} = 2$ at the point $(1, 1)$ is: