If the line $x + my + am^2 = 0$ is tangent to the parabola $y^2 = 4ax$,find the point of contact.

The locus of the middle points of all chords of the parabola $y^2 = 4ax$ passing through the vertex is

The number of normals drawn to the parabola $y^2=4x$ from the point $(1,0)$ is

Let the point $P$ of the focal chord $PQ$ of the parabola $y^2=16x$ be $(1, -4)$. If the focus of the parabola divides the chord $PQ$ in the ratio $m:n$,where $\operatorname{gcd}(m, n)=1$,then $m^2+n^2$ is equal to:

The coordinates of the focus of the parabola $5x^2 = -12y$ are

$A$ point $P(x, y)$ moves such that its distance from the point $(a, 0)$ is always equal to its distance from the line $x + a = 0$. The locus of the point is: