The line $y = 2x + c$ is tangent to the parabola $y^2 = 4x$,then $c = $

The equation of the parabola with focus $(0,0)$ and directrix $x+y=4$ is

The length of the latus-rectum of the parabola whose focus is $\left( \frac{u^2}{2g} \sin 2\alpha, -\frac{u^2}{2g} \cos 2\alpha \right)$ and directrix is $y = \frac{u^2}{2g}$,is

An equilateral triangle is inscribed in the parabola $y^{2}=4ax$,where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

The equation of the lines joining the vertex of the parabola $y^2 = 6x$ to the points on it whose abscissa is $24$ is:

If a parabolic reflector is $20 \, cm$ in diameter and $5 \, cm$ deep,find the focus.