The length of the latus rectum of the conic $25[(x-2)^2+(y-3)^2]=(3x-4y+7)^2$ is

If the tangent to the parabola $y^{2} = 4ax$ at point $P(p, q)$ is perpendicular to the tangent at another point $Q$,find the coordinates of $Q$.

The equation of the tangent to the parabola $y^{2}=4x$ inclined at an angle of $\frac{\pi}{4}$ to the positive direction of $x$-axis is:

If the tangents at $P$ and $Q$ on a parabola meet at $T$,then $SP, ST$ and $SQ$ are in

If $(x_1, y_1)$ and $(x_2, y_2)$ are the endpoints of a focal chord of the parabola $y^2 = 4ax$,then what is the square of the $G.M.$ of $x_1$ and $x_2$?

If the perpendicular distance from the focus of a parabola $y^2=4ax$ to its directrix is $\frac{3}{2}$,then the equation of the normal drawn at $(4a, -4a)$ is