Find the point where the normal at the point $(4, 4)$ intersects the parabola $y^2 = 4x$ again.

If a normal chord of a parabola $y^2 = 4ax$ subtends a right angle at the origin,then the slope of that normal chord is

The equation of the parabola whose vertex and focus are $(0, 4)$ and $(0, 2)$ respectively,is

What is the length of the chord of contact of the tangents drawn from the point $(-2, -1)$ to the parabola $y^2 = 4x$?

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:

If the focal distance of a point $P(2, y_1)$ on the parabola $y^2=kx$ is $3$,then the equation of the tangent drawn at $P$ to the given parabola is