The equation of the tangent to the parabola $y^2=12x$ at the point $(3,-6)$ is:

The position of a moving point in the $XY$-plane at time $t$ is given by $\left( (u \cos \alpha)t, (u \sin \alpha)t - \frac{1}{2}gt^2 \right)$,where $u, \alpha, g$ are constants. The locus of the moving point is

The minimum distance between the parabola $y^2 = 8x$ and its image with respect to the line $x + y + 4 = 0$ is:

The point on the parabola $y^2 = 8x$ at which the normal is inclined at $60^\circ$ to the $x$-axis has the coordinates:

The maximum possible area bounded by the parabola $y=x^2+x+10$ and a chord of the parabola of length $1$ is

What are the coordinates of the endpoints of the latus rectum of the parabola $(y - 1)^2 = 4(x + 1)$?