Find the equation of the parabola that satisfies the following conditions: Focus $(6, 0)$,directrix $x = -6$.

What is the equation of the chord of contact drawn from the point $(2, 4)$ to the parabola $y^2 = 4x$?

Find the coordinates of the point of intersection of the tangents at the endpoints of the latus rectum of the parabola $y^2 = 4x$.

If the line $2x + 3y + n = 0$ is a tangent to the parabola $y^2 = 8x$,then the equation of the normal drawn at the point $(2n, 4\sqrt{n})$ to the parabola $y^2 = 8x$ is

The parabola with focus at $(4, -3)$ and vertex at $(4, -1)$ is

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