The equation of the parabola with its vertex at the origin,axis on the $y$-axis and passing through the point $(6, -3)$ is

Let $A(1, 2)$ be a point on the parabola $y^2 = 4x$. Let $B$ and $C$ be the points of intersection of this parabola with a variable line passing through the point $P(5, -2)$. Then the $\Delta ABC$ (if it exists):

If the line $y = 2x + k$ is a tangent to the curve $x^2 = 4y$,then $k$ is equal to

$A$ parabola passing through the point $(-4, -2)$ has its vertex at the origin and the $y$-axis as its axis. The length of the latus rectum of the parabola is:

If ${x^2} + 6x + 20y - 51 = 0$,then the axis of the parabola is

The line $y = 6x + 1$ touches the parabola $y^2 = 24x$. The coordinates of a point $P$ on this line,from which the tangent to $y^2 = 24x$ is perpendicular to the line $y = 6x + 1$,is