If $y^2=16x$ is the given parabola,then the point of intersection of the focal chord passing through the point $(2,2)$ and the double ordinate of length $24$ is

Let $l$ be the directrix of the parabola $9y^2+12y+9x-14=0$ and $l_1$ be the line passing through the vertex of this parabola and the origin. If $(h, k)$ is the point of intersection of $l$ and $l_1$,then $h+k=$

What is the equation of the tangent to the curve $x^2 = -4y$ at the point $(-4, -4)$?

The length of the latus rectum of a parabola,whose vertex and focus are on the positive $x$-axis at a distance $R$ and $S$ $(S > R)$ respectively from the origin,is:

If a normal chord of the parabola $y^2 = 4ax$ subtends a right angle at the vertex,find the slope of the line joining the vertex and the endpoint of the normal.

Let $PQ$ be a focal chord of the parabola $y^2=4ax$. The tangents to the parabola at $P$ and $Q$ meet at a point $R$ lying on the line $y=2x+a$,where $a > 0$.
$1.$ The length of the chord $PQ$ is:
$(A)$ $7a$ $(B)$ $5a$ $(C)$ $2a$ $(D)$ $3a$
$2.$ If the chord $PQ$ subtends an angle $\theta$ at the vertex of the parabola $y^2=4ax$,then $\tan \theta$ is:
$(A)$ $\frac{2}{3}\sqrt{7}$ $(B)$ $\frac{-2}{3}\sqrt{7}$ $(C)$ $\frac{2}{3}\sqrt{5}$ $(D)$ $\frac{-2}{3}\sqrt{5}$