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