The equation of the tangent to the parabola $y^{2}=16x$ at the point $P(3, 6)$ is:

Let $(x, y)$ be any point on the parabola $y^2 = 4x$. Let $P$ be the point that divides the line segment from $(0, 0)$ to $(x, y)$ in the ratio $1:3$. Then the locus of $P$ is

The ends of the latus rectum of the parabola $x^2 + 8y = 0$ are

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:

Find the equation of the directrix of the parabola $y^2 = 12x$.

What is the common tangent to the parabola $y^{2} = 8ax$ and the circle $x^{2} + y^{2} = 2a^{2}$?