$x - 2 = t^2$ and $y = 2t$ are the parametric equations of which parabola?

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

$A$ normal chord of the parabola $y^2 = 4x$ subtending a right angle at the vertex makes an acute angle $\theta$ with the $x$-axis. Then $\theta$ is equal to:

The parabola $x^2=4ay$ makes an intercept of length $\sqrt{40}$ units on the line $y=2x+1$. Find the value of $4a$.

If three points $P, Q, R$ on the parabola $y^2 = 4ax$ are such that their ordinates are in geometric progression,then the tangents at $P$ and $R$ intersect on:

Let chord $PQ$ of length $3\sqrt{13}$ of the parabola $y^2 = 12x$ be such that the ordinates of points $P$ and $Q$ are in the ratio $1:2$. If the chord $PQ$ subtends an angle $\alpha$ at the focus of the parabola, then $\sin \alpha$ is equal to: