Math Problem Solver

The graph of the equation $2 x = {y}^{2} - 4$ is a parabola.

The coordinates of its vertex are: $\left(-2, 0\right)$

The coordinates of its focus are: $\left(- \frac{3}{2}, 0\right)$

The directrix has equation: $2 x + 5 = 0$.

The parabola has parameterization: $$\begin{aligned}x\left(\theta\right) &= -2 + \frac{\theta^{2}}{2}\\y\left(\theta\right) &= \theta\end{aligned}$$