The length of the latus rectum of the parabola $9x^2 - 6x + 36y + 19 = 0$ is:

The length of the latus rectum of the parabola $9x^2 + 16y^2 + 24xy - 4x + 3y = 0$ is

If two normals are drawn from a point to the parabola $y^{2} = 4ax$ such that they make angles $\alpha$ and $\beta$ with the axis,and $\tan \alpha \cdot \tan \beta = 2$,find the locus of the point.

If a normal is drawn to the parabola $y^2 = 4ax$ at the point $(2a, 2\sqrt{2}a)$,what is the length of the normal chord?

The focus of the parabola $4y^2 - 6x - 4y = 5$ is

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