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

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. If another tangent is drawn to the parabola from a point on this line such that it is perpendicular to the given tangent,find the point.

What is the value of the parameter $t$ for the point $(2, 6)$ on the parabola $y^2 = 18x$?

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

The tangent drawn at any point $P$ to the parabola ${y^2} = 4ax$ meets the directrix at the point $K$. Then the angle which $KP$ subtends at its focus is ............. $^\circ$.

If the line $y=2x+k$ is a normal to the parabola $y^2=4x$,then $k=$