If $x = my + c$ is a normal to the parabola ${x^2} = 4ay$,then the value of $c$ is

If the focus of a parabola divides a focal chord of the parabola into segments of lengths $5$ and $3$ units,then the length of the latus rectum of that parabola is:

Let $PQ$ be a double ordinate of the parabola $y^2 = -4x$,where $P$ lies in the second quadrant. If $R$ divides $PQ$ in the ratio $2 : 1$,then the locus of $R$ is:

If the line $y = 4 + kx$,$k > 0$,is the tangent to the parabola $y = x - x^{2}$ at the point $P$ and $V$ is the vertex of the parabola,then the slope of the line through $P$ and $V$ is

From a point $(d, 0)$,three normals are drawn to the parabola $y^{2} = x$. Then:

Let $O$ be the vertex of the parabola $x^{2}=4y$ and $Q$ be any point on it. Let the locus of the point $P$,which divides the line segment $OQ$ internally in the ratio $2:3$,be the conic $C$. Then the equation of the chord of $C$,which is bisected at the point $(1, 2)$,is: