The normal drawn at a point $(2, -4)$ on the parabola $y^2 = 8x$ cuts the same parabola again at $(\alpha, \beta)$. Then $\alpha + \beta =$

If $P$ is a point on the parabola $y^2=8x$ and $A$ is the point $(1,0)$,then the locus of the mid-point of the line segment $AP$ is

If a circle with its centre at the focus of the parabola $y^2 = 2px$ is such that it touches the directrix of the parabola,then a point of intersection of the circle and the parabola is

If ${y_1}$ and ${y_2}$ are the ordinates of two points $P$ and $Q$ on the parabola ${y^2 = 4ax}$ and ${y_3}$ is the ordinate of the point of intersection of the tangents at $P$ and $Q$,then:

The point of intersection of the latus rectum and axis of the parabola $y^2+4x+2y-8=0$ is

If the normals at two points on the parabola $y^2 = 4ax$ meet on the parabola,then what is the product of the ordinates of these two points?