The equation of the parabola whose vertex is at $(2, -1)$ and focus at $(2, -3)$ is

Consider the parabola $y^2=4x$. Let $S$ be the focus of the parabola. $A$ pair of tangents drawn to the parabola from the point $P=(-2,1)$ meet the parabola at $P_1$ and $P_2$. Let $Q_1$ and $Q_2$ be points on the lines $SP_1$ and $SP_2$ respectively such that $PQ_1$ is perpendicular to $SP_1$ and $PQ_2$ is perpendicular to $SP_2$. Then,which of the following is/are $TRUE$?
$(A)$ $SQ_1=2$
$(B)$ $Q_1Q_2=\frac{3\sqrt{10}}{5}$
$(C)$ $PQ_1=3$
$(D)$ $SQ_2=1$

For any non-zero real value of $m$,the equation of the parabola to which the line $m x-y+10+m^2=0$ is a tangent,is

If a normal chord at a point $t (\neq 0)$ on the parabola $y^2 = 9x$ subtends a right angle at its vertex,then $t =$

Tangents drawn at the ends of any focal chord of a parabola $y^2 = 4ax$ intersect on the line

What is the polar of the focus of a parabola?