If $a \neq 0$ and the line $2bx + 3cy + 4d = 0$ passes through the points of intersection of the parabolas $y^2 = 4ax$ and $x^2 = 4ay$,then

The parametric equations of the curve $y^2 = 8x$ are

Let $A(1, 2)$ be a point on the parabola $y^2 = 4x$. Let $B$ and $C$ be the points of intersection of this parabola with a variable line passing through the point $P(5, -2)$. Then the $\Delta ABC$ (if it exists):

$A$ particle is moving in the $xy$-plane along a curve $C$ passing through the point $(3, 3)$. The tangent to the curve $C$ at the point $P$ meets the $x$-axis at $Q$. If the $y$-axis bisects the segment $PQ$,then $C$ is a parabola with

If the tangent drawn at the point $P(4,8)$ to the parabola $y^2=16x$ meets the parabola $y^2=16x+80$ at $A$ and $B$,then the mid-point of $AB$ is

If the normals at two points $P$ and $Q$ of a parabola $y^2 = 4ax$ intersect at a third point $R$ on the curve,then the product of the ordinates of $P$ and $Q$ is (in $a^2$)