What is the polar of the focus of a parabola?

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:

If the line $x + y = k$ is a normal to the parabola $y^2 = 4x$,find the value of $k$.

If the focus of a parabola is $(0,-3)$ and its directrix is $y=3$,then its equation is

Match the items given in List-$A$ with those of the items of List-$B$:

List-$A$	List-$B$
$(A)$. The vertex of the parabola $y^2+4x-2y+3=0$ is	$(I)$. $\left(\frac{5}{4}, 1\right)$
$(B)$. The vertex of the parabola $x^2+8x+12y+4=0$ is	$(II)$. $\left(1, \frac{5}{4}\right)$
$(C)$. The focus of the parabola $y^2-x-2y+2=0$ is	$(III)$. $\left(-\frac{1}{2}, 1\right)$
$(D)$. The focus of the parabola $x^2-2x-8y-23=0$ is	$(IV)$. $(1, -1)$
	$(V)$. $(-4, 1)$

The correct match is:

The locus of the points of intersection of perpendicular normals to the parabola $y^2=4ax$ is