If two tangents drawn from a point $P$ to the parabola $y^2 = 4x$ are at right angles,then the locus of $P$ is:

If a focal chord of the parabola $y^2 = 4ax$ makes an angle $\theta$ with its axis,then the length of the perpendicular from the vertex to this chord is......

At what point on the parabola $y^2 = 4x$ does the normal make equal angles with the coordinate axes?

Find the locus of the midpoints of the chords of the parabola $x^2 + 4y = 0$ which pass through its focus.

If the line $x + y = k$ is a normal to the parabola $y^2 = 4x$,find the value of $k$.

Let a circle tangent to the directrix of a parabola $y^2 = 2ax$ have its center coinciding with the focus of the parabola. Then the points of intersection of the parabola and the circle are