If the normals at points $t_1$ and $t_2$ on the parabola $y^2 = 4ax$ intersect again on the parabola,then what is the value of $t_1t_2$?

Find the equation of the normal to the parabola $y^2 + 12x = 0$ at the upper end of its latus rectum.

The equation of the tangent to the parabola $y = (x - 3)^2$ parallel to the chord joining the points $(3, 0)$ and $(4, 1)$ is:

If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola,then its equation is

$A$ tangent is drawn to the parabola $y^{2}=6x$ which is perpendicular to the line $2x+y=1$. Which of the following points does $NOT$ lie on it?

If the focus divides a focal chord of the parabola $y^2 = 16x$ into $2$ parts having lengths $a$ and $c$,such that $a, b, c$ are in $H.P.$,then the value of $b$ is equal to: