Parabola in standard position

Theorem 3.1 (Parabola in standard position). The parabola with focus \((h + p, k)\) and directrix \(x = h - p\), where \(p \neq 0\), is

Its vertex is \((h, k)\) and its axis is the line \(y = k\). Exchanging the roles of \(x\) and \(y\) gives the parabola \((x - h)^2 = 4p(y - k)\) with a vertical axis.