If the focus of the parabola is $(3, -4)$ and the directrix is $y - 4 = 0,$ then the equation of the parabola is :-

The area of the triangle formed by the lines joining the vertex of the parabola $x^2=12y$ to the ends of its latus rectum is equal to $...$ sq. units.

If the focal chord drawn through the point $P(5,5)$ to the parabola $y^2=5x$ meets the parabola again at the point $Q$,then the tangent drawn to this parabola at $Q$ meets the axis of the parabola at the point

What is the vertex of the parabola $x^2 - 8y - x + 19 = 0$?

What is the slope of the tangent drawn from the point $(4, 10)$ to the parabola $y^2 = 9x$?

An equilateral triangle is inscribed in the parabola $y^2 = 4ax$ such that one of its vertices is at the origin $(0, 0)$ and the other two vertices lie on the parabola. The length of its side is equal to