The equation of the tangent to the parabola $y^2=8x$,which is parallel to the line $4x-y+3=0$,is

The tangents to the curve $y = (x - 2)^2 - 1$ at its points of intersection with the line $x - y = 3$ intersect at the point:

The parabolas $ax^2 + 2bx + cy = 0$ and $dx^2 + 2ex + fy = 0$ intersect on the line $y = 1$. If $a, b, c, d, e, f$ are positive real numbers and $a, b, c$ are in $G.P.$,then

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

The condition that the line $ax + by + c = 0$ is tangent to the parabola $y^2 = 4ax$ is:

If the line $x + my + am^2 = 0$ is tangent to the parabola $y^2 = 4ax$,find the point of contact.