$3y^{2}$-7x+9=4y
You asked:
Investigate the equation: \(3 \cdot {y}^{2} - 7 x + 9 = 4 y\).
MathBot Answer:
The graph of the equation \(3 \cdot {y}^{2} - 7 x + 9 = 4 y\) is a parabola.
The coordinates of its vertex are: \(\left(\frac{23}{21}, \frac{2}{3}\right)\)
The coordinates of its focus are: \(\left(\frac{47}{28}, \frac{2}{3}\right)\)
The directrix has equation: \(\frac{12 x}{7} - \frac{43}{49} = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{23}{21} + \frac{3 \theta^{2}}{7}\\y\left(\theta\right) &= \frac{2}{3} + \theta\end{aligned}\]