The equation of the normal to the parabola $y^{2} = x + a$ with slope $m$ is .....

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

If the tangent at a point $P,$ with parameter $t,$ on the curve $x = 4t^2 + 3, y = 8t^3 - 1, t \in R,$ meets the curve again at a point $Q,$ then the coordinates of $Q$ are

The axis of a parabola lies along the $x$-axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin on the positive $x$-axis,then which of the following points does not lie on it?

At what point on the parabola $y^2 = 4x$ does the normal make equal angles with the coordinate axes?

Let the length of the focal chord $PQ$ of the parabola $y^2=12x$ be $15$ units. If the distance of $PQ$ from the origin is $p$,then $10p^2$ is equal to: