The eccentricity of the parabola $x^2 - 4x - 4y + 4 = 0$ is

What is the vertex of the parabola $9x^2 - 6x + 36y + 9 = 0$?

The slope of the line touching both the parabolas $y^2 = 4x$ and $x^2 = -32y$ is

Find the length of the latus rectum of the parabola whose focus is $(2, 3)$ and the directrix is the line $x - 4y + 3 = 0$.

If a focal chord of the parabola $y^2 = 4ax$ makes an angle $\theta$ with its axis,then the length of the perpendicular from the vertex to this chord is......

The point on the curve $x^{2}=2 y$ which is nearest to the point $(0,5)$ is