If the segment intercepted by the parabola $y^2 = 4ax$ with the line $lx + my + n = 0$ subtends a right angle at the vertex,then

Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8x$. If the set of all values of $\alpha$,for which three chords of the circle $C$ on three distinct lines passing through the point $(\alpha, 0)$ are bisected by the parabola $P$,is the interval $(p, q)$,then $(2q-p)^2$ is equal to.............

The equation of the tangent to the parabola $y^2 = 4ax$ at the point $(3, 2)$ is . . . .

Find the equation of the tangent to the parabola $x^2 = y$ at one of the endpoints of its latus rectum in the first quadrant.

If the line $y = 2x + k$ is a tangent to the curve $x^2 = 4y$,then $k$ is equal to

If the tangent at a point $P$ on a parabola makes an angle $\alpha$ with its focal distance,then the angle between the tangent and the axis of the parabola is: