The focal distance of a point $(5, 5)$ on the parabola $x^2 - 2x - 4y + 5 = 0$ is

If $ax^2+2hxy+by^2-82x+98y+144=0$ is the equation of a parabola with focus $(2,-3)$ and directrix $3x-2y+5=0$,then $ax^2+2hxy+by^2=0$ represents

For the parabola $y^2 = 8(x - 3)$,let $P$ be a point on it. Let $M$ be the foot of the perpendicular from $P$ to the directrix,and $S$ be the focus of the parabola. If $\triangle SPM$ is an equilateral triangle,find the length of each side of the triangle.

Normals at $P$,$Q$,and $R$ are drawn to the parabola $y^2 = 4x$ which intersect at the point $(3, 0)$. Then,the triangle $\Delta PQR$ is:

The point $(3,4)$ is the focus and $2x - 3y + 5 = 0$ is the directrix of a parabola. Its latus rectum is:

If the tangents at the endpoints $P$ and $Q$ of a chord of a parabola meet at point $T$,then the distances of points $P, T, Q$ from the focus of the parabola are in which progression?