4y=x $^{2}$
You asked:
Investigate the equation: \(4 y = {x}^{2}\).
MathBot Answer:
The graph of the equation \(4 y = {x}^{2}\) is a parabola.
The coordinates of its vertex are: \(\left(0, 0\right)\)
The coordinates of its focus are: \(\left(0, 1\right)\)
The directrix has equation: \(y + 1 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= \frac{\theta^{2}}{4}\end{aligned}\]