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

$A$ point $P$ moves such that the sum of the angles which the three normals drawn from $P$ to the standard parabola $y^2 = 4ax$ make with the axis of the parabola is constant. Then the locus of $P$ is:

Find the equation of the tangent at the vertex of the parabola $4y^2 + 6x = 8y + 7$.

What is the vertex of the parabola $x^2 + 4x + 2y - 7 = 0$?

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

Find the length of the chord of the parabola $y^2 = 4x$ which passes through the vertex and makes an angle of $30^{\circ}$ with the $x$-axis. (in $\sqrt{3}$)