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

The number of normals drawn to the parabola $y^2=4x$ from the point $(1,0)$ is

Let $M$ be the foot of the perpendicular from a point $P$ on the parabola $y^2=8(x-3)$ onto its directrix and let $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,then $P$ is equal to

If the parabola $x^{2}=ay$ makes an intercept of length $\sqrt{40}$ units on the line $y-2x=1$,then $a$ is equal to

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

The equation of a curve in polar coordinates is $\frac{l}{r} = 2 \sin^2 \frac{\theta}{2}$. This equation represents: