The distance of the point $(6, 4 \sqrt{3})$ from the focus of the parabola $y^2 = 8x$ is:

If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola,then its equation is

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

Tangents are drawn at three points $P(t_1), Q(t_2), R(t_3)$ on the parabola $y^2 = x$. Let these tangents intersect each other at the points $L, M, N$. If $t_1 = 2, t_2 = -4, t_3 = 6$,then the area of the triangle $LMN$ is

The area of the triangle formed by the lines joining the vertex of the parabola $x^{2}=12y$ to the ends of the latus rectum is

If two normals to the parabola $y^2 = 4x$ passing through the point $(15, 12)$ are $4x + y = 72$ and $3x - y = 33$,find the third normal.