If the normal at the point $t_1$ (i.e.,at $(at_1^2, 2at_1)$) on the parabola $y^2 = 4ax$ meets the parabola again at the point $t_2$,then $t_1t_2$ is equal to:

The locus of the middle points of all chords of the parabola $y^2 = 4ax$ passing through the vertex is

What is the equation of the tangent to the parabola $y^2 = 12x$ at the upper end of its latus rectum?

Let $x=2t, y=\frac{t^2}{3}$ be a conic. Let $S$ be the focus and $B$ be the point $(0, \alpha)$ on the axis of the conic such that $SA \perp BA$,where $A$ is any point $(2t, \frac{t^2}{3})$ on the conic. If $k$ is the ordinate of the centroid of $\Delta SAB$,then $\lim_{t \rightarrow 1} k$ is equal to

The parametric equations of the parabola $y^2 - 12x - 2y - 11 = 0$ are:

The point on the curve $x^{2}=2 y$ which is nearest to the point $(0,5)$ is