Find the equation of the parabola that satisfies the following conditions: Vertex $(0, 0)$; focus $(3, 0)$.

Consider the parabola with vertex $\left(\frac{1}{2}, \frac{3}{4}\right)$ and the directrix $y=\frac{1}{2}$. Let $P$ be the point where the parabola meets the line $x=-\frac{1}{2}$. If the normal to the parabola at $P$ intersects the parabola again at the point $Q$,then $(PQ)^{2}$ is equal to :

What is the slope of the tangents drawn from $(3, 8)$ to the parabola $y^2 = -12x$?

The point on the parabola $y^{2}=64x$ which is nearest to the line $4x+3y+35=0$ has coordinates

Find the parametric coordinates of any point on the parabola whose focus is $(0, 1)$ and directrix is $x + 2 = 0$.

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