Prove that the focal distance of the point `(x ,y)` on the parabola `x^2-8x+16 y=0` is `|y+5|`

Find the sum of the focal distances of any point on the ellipse 9x^2+16 y^2=144.

The equation of the directrix of the parabola y^(2)=-8x is

Three normals are drawn from the point (7, 14) to the parabola x^2-8x-16 y=0 . Find the coordinates of the feet of the normals.

Find the shortest distance of the point (0, c) from the parabola y=x^2 , where 0lt=clt=5 .

Find the shortest distance of the point (0, c) from the parabola y=x^2 , where 0lt=clt=5 .

The vertex of the parabola x^(2)=8y-1 is :

The focus of the parabola x^2 -2x +8y + 17=0 is :

A parabola is drawn touching the axis of x at the origin and having its vertex at a given distance k form this axis Prove that the axis of the parabola is a tangent to the parabola x^2=-8k (y-2k) .

Find the shortest distance between the line y=x-2 and the parabola y=x^2+3x+2.

Find the shortest distance between the line y=x-2 and the parabola y=x^2+3x+2.