The equation of the parabola with $(-3, 0)$ as focus and $x + 5 = 0$ as directrix is

At which point does the line $x = my + \frac{a}{m}$ touch the parabola $x^2 = 4ay$?

The maximum number of common normals of $y^2=4ax$ and $x^2=4by$ is equal to

The distance of the point $(6, -2 \sqrt{2})$ from the common tangent $y = mx + c$ $(m > 0)$ of the curves $x = 2y^2$ and $x = 1 + y^2$ is

If the line $2x + 3y + n = 0$ is a tangent to the parabola $y^2 = 8x$,then the equation of the normal drawn at the point $(2n, 4\sqrt{n})$ to the parabola $y^2 = 8x$ is

Let $A, B$ and $C$ be three points on the parabola $y^2=6x$ and let the line segment $AB$ meet the line $L$ through $C$ parallel to the $x$-axis at the point $D$. Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ and $B$ on $L$. Then $\left(\frac{AM \cdot BN}{CD}\right)^2$ is equal to...........