If two tangents drawn from a point $P$ to the parabola $y^{2}=16(x-3)$ are at right angles,then the locus of point $P$ is :

The tangents to the parabola $y^2 = 4ax$ make angles $\theta_1$ and $\theta_2$ with the positive $x$-axis. If $\cot \theta_1 + \cot \theta_2 = c$,then the locus of their point of intersection is

If a double ordinate of the parabola $y^2 = 4ax$ has a length of $8a$,then the angle between the lines joining the vertex of the parabola to the ends of this double ordinate is ............... $^\circ$.

The equation of the tangent to the parabola $y^2 = 16x$,which is perpendicular to the line $y = 3x + 7$,is

If a normal chord of the parabola $y^2 = 4ax$ subtends a right angle at the vertex,find the slope of the line joining the vertex and the endpoint of the normal.

If a perpendicular drawn through the vertex $O$ of the parabola $y^2=4ax$ to any of its tangent meets the tangent at $N$ and the parabola at $M$,then $ON \cdot OM=$