The equation of the axis of the parabola $x^2 - 4x - 3y + 10 = 0$ is:

The distance of the point $(6, -2 \sqrt{2})$ from the common tangent $y = mx + c$ $(m > 0)$ of the curves $x = 2y^2$ and $x = 1 + y^2$ is

If the vertex of a parabola is $(2, -1)$ and the equation of its directrix is $4x - 3y = 21$,then the length of its latus rectum is

Let $P(\alpha, \beta)$ be a point on the parabola $y^2 = 4x$. If $P$ also lies on the chord of the parabola $x^2 = 8y$ whose midpoint is $(1, 5/4)$,then $(\alpha - 28)(\beta - 8)$ is equal to:

The parabola $x^2=4ay$ makes an intercept of length $\sqrt{40}$ units on the line $y=2x+1$. Find the value of $4a$.

What is the vertex of the parabola $y^2 + 6x - 2y + 13 = 0$?