The Cartesian equation of the parabola $x = -2 + 2t^2$,$y = 2 + 4t$ is

The intercepts of the focal chord (which is a part of the latus rectum) to the parabola $y^{2}=4ax$ are $b$ and $k$. Then $k$ is equal to:

The locus of the mid-point of the line segment joining the focus and any point on the parabola $y^{2}=4ax$ is a parabola. Find the equation of its directrix.

The angle between the parabolas $y^2 = 4(x-1)$ and $x^2 + 4(y-3) = 0$ at the common end of their latus rectum is:

In which quadrant does the vertex of the parabola $y^2 + 2y + x = 0$ lie?

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 $a^2$)