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

Find the equation of the common tangent to the parabolas $y = x^2$ and $y = -(x - 2)^2$.

The angle between the tangents drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

The Cartesian equation of the parabola $x = -2 + 2t^2$,$y = 2 + 4t$ is

If the focal chord drawn through the point $P(5,5)$ to the parabola $y^2=5x$ meets the parabola again at the point $Q$,then the tangent drawn to this parabola at $Q$ meets the axis of the parabola at the point