If the focus divides a focal chord of the parabola $y^2 = 16x$ into $2$ parts having lengths $a$ and $c$,such that $a, b, c$ are in $H.P.$,then the value of $b$ is equal to:

If two normals to a parabola $y^2 = 4ax$ intersect at right angles,then the chord joining their feet passes through a fixed point whose coordinates are:

Two perpendicular tangents to the parabola $y^2 = 4ax$ always intersect on the line:

Let $P$ be the point on the parabola ${y^2} = 8x$ which is at a minimum distance from the centre $C$ of the circle ${x^2} + {(y + 6)^2} = 1$. Then the equation of the circle,passing through $C$ and having its centre at $P$,is:

The equation of a curve in polar coordinates is $\frac{l}{r} = 2 \sin^2 \frac{\theta}{2}$. This equation represents:

If $mx - y + c = 0$ is a normal at a point $P$ on the parabola $y^2 = 16x$ and the focal distance of $P$ is $40$ units,then $|c| =$