The vertex of the parabola $x^2 + 8x + 12y + 4 = 0$ is

If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola,then its equation is

The point on the curve $x^{2}=2 y$ which is nearest to the point $(0,5)$ is

What is the maximum number of normals that can be drawn from any interior point to a parabola?

Let $A$ be the vertex and $L$ be the length of the latus rectum of the parabola $y^2 - 2y - 4x - 7 = 0$. Find the equation of the parabola with $A$ as the vertex,$2L$ as the length of the latus rectum,and the axis at right angles to that of the given curve.

For what value of $k$ does the line $2y - x + k = 0$ touch the parabola $x^2 + 4y = 0$?