Equation of the normal to the curve $y=x^2+x$ at the point $(1,2)$ is

Find the points on the curve $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$ at which the tangents are parallel to the $x$-axis.

If $T$ is the length of the subtangent drawn at any point on the curve $3 y^2 = 4 x^3$ and $N$ is the length of the subnormal at the same point,then $(\beta T)^2 =$

The equation of the tangent to the curve $y = 3x^3 - 3x^2 + x$ at $x = 1$ is

If the angle made by the tangent at the point $(x_{0}, y_{0})$ on the curve $x=12(t+\sin t \cos t)$,$y =12(1+\sin t )^{2}$,$0 < t < \frac{\pi}{2}$,with the positive $x$-axis is $\frac{\pi}{3}$,then $y_{0}$ is equal to

If $\frac{k}{\alpha^3}$ is the length of the subnormal at any point $P(\alpha, y)$ on the curve $x^2-a^2=\frac{x^2 y^2}{a^2}$, then $k=$