If the normal to the parabola $y^2 = 4ax$ at the point $(a, 2a)$ meets the parabola again at the point $(at^2, 2at)$,then what is the value of $t$?

If a normal chord at a point $t$ on the parabola $y^2=4ax$ subtends a right angle at the vertex,then $t^2$ equals to

If tangents are drawn from the point $(-1, 2)$ to the parabola $y^2 = 4x$, what is the area of the triangle formed by the chord of contact and the tangents (in $\sqrt{2}$)?

The angle of intersection between the curves $x^2 = 8y$ and $y^2 = 8x$ at the origin is

What is the area of the triangle formed by the vertex of the parabola $x^2 = 12y$ and the endpoints of its latus rectum (in square units)?

The line $x - y + 2 = 0$ touches the parabola $y^2 = 8x$ at the point