Find the co-ordinates of a point of the parabola ${\mathrm{y}}^2=8\mathrm{x}$ having focal  distance $10$. 

Find the equation of the tangent to the parabola ${\mathrm{y}}^2=9\mathrm{x}$ at the point $(4,-6)$ on it.

Find the equation of the tangent to the parabola ${\mathrm{y}}^2=8\mathrm{x}$ at $\mathrm{t}=1$ on it.

Find the equations of the tangents to the parabola ${\mathrm{y}}^2=9\mathrm{x}$ through the point $(4,10)$.
 

Show that the two tangents drawn to the parabola ${\mathrm{y}}^2=24\mathrm{x}$ from the point (-6,9) are at the right angle.

Find the equation of the tangent to the parabola ${\mathrm{y}}^2=8\mathrm{x}$ which is parallel to the line $2 \mathrm{x}+2 \mathrm{y}+5=0 .$ Find its point of contact.
 

A line touches the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=2$ and the parabola ${\mathrm{y}}^2=\mathrm{x}.$ Show that its equation is $\mathrm{y}=\pm (\mathrm{x}+2)$

Two tangents to the parabola ${\mathrm{y}}^2=8\mathrm{x}$ meet the tangent at the vertex in $\mathrm{P}$ and $\mathrm{Q}$ If $\mathrm{PQ}=4,$ prove that the locus of the point of intersection of the two tangents is ${\mathrm{y}}^2=8(\mathrm{x}+2)$

The slopes of the tangents drawn from $\mathrm{P}$ to the parabola ${\mathrm{y}}^2=4\mathrm{ax}$ are ${\mathrm{m}}_1$ and ${\mathrm{m}}_2,$ show that
${\mathrm{m}}_1-{\mathrm{m}}_2=\mathrm{k}$