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

The point of intersection of the normals to the parabola $y^2 = 4x$ at the ends of its latus rectum is

$A$ point $P(x, y)$ moves such that its distance from the point $(a, 0)$ is always equal to its distance from the line $x + a = 0$. The locus of the point is:

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

If the equation of a system of parallel chords of the parabola $y^2 = \frac{2}{3}x$ is $y + 2x + 1 = 0$,find its diameter.

The equation of the parabola whose focus is the point $(0, 0)$ and the tangent at the vertex is $x - y + 1 = 0$ is