The angle between the tangents drawn to the parabola $y^{2}=12x$ from the point $(-3, 2)$ is (in $^{\circ}$)

If the line $x + my + am^2 = 0$ is tangent to the parabola $y^2 = 4ax$,find the point of contact.

$A$ set of parallel chords of the parabola $y^2 = 4ax$ have their mid-points on:

Let $PQ$ be a double ordinate of the parabola $y^2 = -4x$,where $P$ lies in the second quadrant. If $R$ divides $PQ$ in the ratio $2 : 1$,then the locus of $R$ is:

If one end of a focal chord of the parabola $y^2=8x$ is $\left(\frac{1}{2}, 2\right)$,then the length of the focal chord is $........$ units.

The equation of the line passing through the point $(1/2, 2)$ and tangent to the parabola $y = -\frac{x^2}{2} + 2$ and secant to the curve $y = \sqrt{4 - x^2}$ is