(y-1)^2 = 12(x-4)
You asked:
Investigate the equation: \({\left( y - 1 \right)}^{2} = 12 \cdot \left(x - 4\right)\).
MathBot Answer:
The graph of the equation \({\left( y - 1 \right)}^{2} = 12 \cdot \left(x - 4\right)\) is a parabola.
The coordinates of its vertex are: \(\left(4, 1\right)\)
The coordinates of its focus are: \(\left(7, 1\right)\)
The directrix has equation: \(\frac{x}{3} - \frac{1}{3} = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= 4 + \frac{\theta^{2}}{12}\\y\left(\theta\right) &= 1 + \theta\end{aligned}\]