The angle between the curves $y^2=4x+4$ and $y^2=36(9-x)$ is (in $^{\circ}$)

Let $f: R \rightarrow R$ be a bijection. $A$ curve represented by $y=f(x)$ is such that $f^{\prime}(x)>0$ for all $x \in R$. The tangent and normal drawn at $P(\alpha, 1)$ on the curve cut the $X$-axis at $A$ and $B$ respectively, and $C$ is the foot of the perpendicular from $P$ onto the $X$-axis. If $P(\alpha, 1)$ is such a point that $AC+CB$ is minimum, then the tangent at $P$ is parallel to the line

The lengths of tangent, subtangent, normal and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are $A, B, C$ and $D$ respectively, then their increasing order is

If the tangent to the curve $2y^3 = ax^2 + x^3$ at the point $(a, a)$ cuts the coordinate axes at $p$ and $q$ such that $p^2 + q^2 = 61$,then what is the value of $a$?

Find the points on the curve $\frac{x^{2}}{9}+\frac{y^{2}}{16}=1$ at which the tangents are parallel to the $y$-axis.

Find the equations of the tangent and normal to the curve $y=x^{4}-6 x^{3}+13 x^{2}-10 x+5$ at the point $(0,5)$.