If the line $lx + my + n = 0$ is tangent to the parabola $y^{2} = 4ax$,then

The normal meets the parabola $y^2 = 4ax$ at a point where the abscissa is equal to the ordinate. Find this point.

Let $R$ be the focus of the parabola $y^2=20x$ and the line $y=mx+c$ intersect the parabola at two points $P$ and $Q$. Let the point $G(10, 10)$ be the centroid of the triangle $PQR$. If $c-m=6$,then $(PQ)^2$ is

The length of the latus rectum of the parabola $2\{(x - 1)^2 + (y - 3)^2\} = (x + y - 1)^2$ is:

The locus of the feet of the perpendiculars drawn from the vertex of the parabola $y^2 = 4ax$ upon all such chords of the parabola which subtend a right angle at the vertex is

If the tangents drawn at the points $P$ and $Q$ on the parabola $y^{2} = 2x - 3$ intersect at the point $R(0, 1)$,then the orthocentre of the triangle $PQR$ is.