Math Problem Solver

The graph of the equation $3 {x}^{2} + 9 b = \left(3 x + 25\right) \left(2 x + 3\right)$ is a parabola.

The coordinates of its vertex are: $\left(- \frac{2581}{108}, - \frac{59}{6}\right)$

The coordinates of its focus are: $\left(- \frac{625}{27}, - \frac{59}{6}\right)$

The directrix has equation: $\frac{4 b}{3} + \frac{2662}{81} = 0$.

The parabola has parameterization: $$\begin{aligned}b\left(\theta\right) &= - \frac{2581}{108} + \frac{\theta^{2}}{3}\\x\left(\theta\right) &= - \frac{59}{6} + \theta\end{aligned}$$