What is the polar of the focus of a parabola?

The equation of the given curve is $x^2-4x+4y-8=0$. Match the following:

List-$I$	List-$II$
$(A)$ Focus	$(I)$ $(4,2)$
$(B)$ Vertex	$(II)$ $(3,2)$
$(C)$ One end of the latus rectum	$(III)$ $(2,3)$
$(D)$ Point of intersection of the axis and directrix	$(IV)$ $(2,4)$
	$(V)$ $(2,2)$

The correct matching is:

Let $S$ denote the locus of the mid-points of those chords of the parabola $y^2=x$,such that the area of the region enclosed between the parabola and the chord is $\frac{4}{3}$. Let $R$ denote the region lying in the first quadrant,enclosed by the parabola $y^2=x$,the curve $S$,and the lines $x=1$ and $x=4$. Then which of the following statements is (are) True?
$(A) \ (4, \sqrt{3}) \in S$
$(B) \ (5, \sqrt{2}) \in S$
$(C)$ Area of $R$ is $\frac{14}{3}-2 \sqrt{3}$
$(D)$ Area of $R$ is $\frac{14}{3}-\sqrt{3}$

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

If two parabolas $y^2 = 4x$ and $x^2 = 32y$ intersect at the point $(16, 8)$ at an angle $\theta$,then what is the value of $\tan \theta$?

What is the area of the triangle formed by the vertex of the parabola $x^2 = 12y$ and the endpoints of its latus rectum (in square units)?