Math Problem Solver

The graph of the equation ${x}^{2} + y = 1$ is a parabola.

The coordinates of its vertex are: $\left(0, 1\right)$

The coordinates of its focus are: $\left(0, \frac{3}{4}\right)$

The directrix has equation: $- 4 y + 5 = 0$.

The parabola has parameterization: $$\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= 1 - \theta^{2}\end{aligned}$$