The line $lx + my + n = 0$ will touch the parabola $y^2 = 4ax$,if

What is the vertex of the parabola $x^2 - 8y - x + 19 = 0$?

The number of points on the parabola $y^2=x$ at which the slope of the normal drawn at the point is equal to the $x$-coordinate of that point is

$A$ normal chord $PQ$ drawn at a point $P$ on the parabola $y^2 = 5x$ subtends a right angle at the vertex. If $P$ lies in the first quadrant,then the other end $Q$ of the normal chord is

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If there are two more normals to this parabola which pass through $(5,0)$,the centroid of the triangle formed by the feet of these three normals is

Normals at $P, Q, R$ are drawn to the parabola $y^2 = 4x$ which intersect at the point $(3, 0)$. Then,$\Delta PQR$ is: