Find the length of the latus rectum of a parabola if $PSQ$ is a focal chord such that $SP = 3$ and $SQ = 2$.

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

The point on the parabola $2y = x^2$ which is nearest to the point $(0, 3)$ is

If $m$ is the slope of the normal to the parabola $y^2 + 4x + 4y = 0$ at the point $(-3, 2)$,which is one of the endpoints of a focal chord,find the value of $m$.

An equilateral triangle is inscribed in the parabola $y^{2}=4ax$,where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

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