The equation of the normal to the parabola $y^{2} = x + a$ with slope $m$ 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?

Find the coordinates of the focus,axis of the parabola,the equation of the directrix,and the length of the latus rectum for $y^{2} = -8x$.

What is the length of the subnormal at any point on the parabola $y^2 = 4ax$?

If $(2, k)$ is a point on the parabola passing through the points $(1, -3), (-1, 5), (0, 2)$ and having its axis parallel to the $Y$-axis,then $k$ is equal to

Let $P$ be the point on the parabola ${y^2} = 8x$ which is at a minimum distance from the centre $C$ of the circle ${x^2} + {(y + 6)^2} = 1$. Then the equation of the circle,passing through $C$ and having its centre at $P$,is: