The angle between tangents to the parabola $y^2 = 4ax$ at the points where it intersects with the line $x - y - a = 0$ is

If the focal chord of the parabola $x^2=12y$ drawn through the point $(3,0)$ intersects the parabola at the points $P$ and $Q$,then the sum of the reciprocals of the abscissae of the points $P$ and $Q$ is

The equation ${y^2} - 2x - 2y + 5 = 0$ represents:

Let $A$ be the focus of the parabola $y^{2}=8x$. Let the line $y=mx+c$ intersect the parabola at two distinct points $B$ and $C$. If the centroid of the triangle $ABC$ is $(\frac{7}{3},\frac{4}{3})$, then $(BC)^{2}$ is equal to:

Let the parabola $y = x^2 + px + q$ passing through the point $(1, -1)$ be such that the distance between its vertex and the $x$-axis is minimum. Then the value of $p^2 + q^2$ 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?