A parabola is the set of all points in the plane equidistant from a fixed point called the focus and a fixed straight line called the directrix. The vertex lies midway between the focus and the directrix.
Let AF = p, where p is the parameter of the parabola.
\[ y^2 = 2px \] This represents a parabola that opens to the right, with the vertex at the origin.
\[ A = \frac{2}{3} l c \] where \( l \) is the chord and \( c \) is the distance from the vertex to the chord.
\[ \varepsilon = \frac{FM}{MK} = 1 \] Unlike ellipses and hyperbolas, a parabola has an eccentricity of exactly 1.
\[ r = x + \frac{p}{2} \] where \( x \) is the x-coordinate of the point on the parabola.
