Let $P_1 : y = -x^2 + 4x + 2$ and $P_2 : x^2 + 5x + \frac{17}{8} = y$ be two parabolas. Then,the number of common tangents of $P_1$ and $P_2$ is:

Let the tangent and normal at any point $P(at^2, 2at)$, $(a > 0)$, on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P, T$ and $G$ is

If a normal is drawn to the parabola $y^2 = 4ax$ at the point $(2a, 2\sqrt{2}a)$,what is the length of the normal chord?

The coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is $4$ are:

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:

$A$ point on the parabola whose focus is $S(1,-1)$ and whose vertex is $A(1,1)$ is