At what point on the parabola $y^2 = 4x$ does the normal make equal angles with the coordinate axes?

What is the area of the triangle formed by the vertex and the endpoints of the latus rectum of the parabola $x^2 = 8y$?

The point on the parabola $y^2 = 8x$ at which the normal is parallel to the line $x - 2y + 5 = 0$ is

The normal at the point $(2, 4)$ to the parabola $y^2 = 4ax$ meets the parabola again at another point. Find the coordinates of this point.

Let a line $y=mx$ $(m>0)$ intersect the parabola $y^{2}=x$ at a point $P$,other than the origin. Let the tangent to it at $P$ meet the $x$-axis at the point $Q$. If $\text{area}(\Delta OPQ)=4$ sq. units,then $m$ is equal to

If the focal chord of the parabola $x^2=12y$ drawn through the point $(3,0)$ intersects the parabola at the points $P$ and $Q$,then the sum of the reciprocals of the abscissae of the points $P$ and $Q$ is