If the normal chord drawn at $(2 a, 2 a \sqrt{2})$ on the parabola $y^2=4 a x$ subtends an angle $\theta$ at its vertex,then $\theta=$ (in $^{\circ}$)

The line $y = 6x + 1$ touches the parabola $y^2 = 24x$. The coordinates of a point $P$ on this line,from which the tangent to $y^2 = 24x$ is perpendicular to the line $y = 6x + 1$,is

The equation of the parabola with focus $(3, 0)$ and the directrix $x + 3 = 0$ is

If $b$ and $c$ are the lengths of the segments of any focal chord of the parabola $y^2 = 4ax$,then what is the length of the semi-latus rectum?

Let $LL^{\prime}$ be the latus rectum and $PQ$ be the focal chord of the parabola $y^2=16x$. If $P=(1,4)$ and $P, L$ lie in the same quadrant,then $LQ=$

If the lines $2x + 3y + 12 = 0$ and $x - y + k = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $k$ is equal to