A parabola is a curve that is the locus of all points in the plane that are equidistant from both the line $L$ (called the directrix) and the point $F$ (called the focus) not in the line.

The equation of a parabola with vertex $\left(x_0,\,y_0\right)$ in Cartesian coordinates is

If the parabola instead opens upwards, its Cartesian equation is

The parametric equations of a parabola with vertex $\left(x_0,\,y_0\right)$ can be given by

If the parabola instead opens upwards, its parametric equations are

In polar coordinates, the equation of a parabola with parameter $a$ and center/centre $\left(0,\, 0\right)$ is given by