The axis of the parabola $x^{2}+2 x y+y^{2}-5 x+5 y-5=0$ is

The equation of the directrix for the parabola $4x^{2}-4x-2y+3=0$ is

Statement $(A)$: If the normal at the ends of the latus rectum of the parabola $y^2 = 4x$ meet the curve again at $P$ and $P'$,then $PP' = 12$ units.
Reason $(R)$: If the normal at $T_1$ to the parabola $y^2 = 4ax$ meets the parabola again at $T_2$,then $T_2 = -T_1 - \frac{2}{T_1}$.

The line among the following which touches the parabola $y^2=4ax$ is

Let the parabola $y = x^2 + px + q$ passing through the point $(1, -1)$ be such that the distance between its vertex and the $x$-axis is minimum. Then the value of $p^2 + q^2$ is:

If the midpoint of a chord is $(-1, 1)$,find the equation of the chord of the parabola $y^2 = 6x$.