The line $y = 2x + c$ is a tangent to the parabola $y^2 = 16x$,if $c$ equals

If the line $7y - 4x = 10$ is a tangent to the parabola $y^2 = 4x$,find the point of contact.

Find the minimum distance from the point $(0, c)$ to the parabola $y = x^2$,where $0 \leq c \leq 5$.

The coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is $4$ are

If $S(a, b)$ is a fixed point and $P(\alpha, \beta)$ is a variable point such that $4[(x-a)^2+(y-b)^2]=(\alpha x+\beta y+7)^2$ represents a parabola,then the locus of $P(\alpha, \beta)$ is

If the line $x + y = k$ is a normal to the parabola $y^2 = 4x$,find the value of $k$.