y^2 − 4y + 12x − 20 = 0
You asked:
Investigate the equation: \({y}^{2} - 4 y + 12 x - 20 = 0\).
MathBot Answer:
The graph of the equation \({y}^{2} - 4 y + 12 x - 20 = 0\) is a parabola.
The coordinates of its vertex are: \(\left(2, 2\right)\)
The coordinates of its focus are: \(\left(-1, 2\right)\)
The directrix has equation: \(- \frac{x}{3} + \frac{5}{3} = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= 2 - \frac{\theta^{2}}{12}\\y\left(\theta\right) &= 2 + \theta\end{aligned}\]