Refer to the diagram shown below.
In the diagram, the two vertices are located at (0, a) and (0, -a).
The equation for the parabola is
[tex] \frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} =1[/tex]
The asymptotes have the equations
[tex]y= \pm \frac{a}{b} x[/tex]
For the given problem,
The vertices are located at (0, +/-10).
Therefore a = 10.
The asymptotes are
[tex]y = \pm \frac{5}{6} x[/tex]
Therefore
[tex] \frac{a}{b} = \frac{10}{b} = \frac{5}{6} \\\\ 5b = 60 \\\\ b =12[/tex]
Answer:
The equation of the parabola is
[tex] \frac{y^{2}}{100} - \frac{x^{2}}{144} =1[/tex]
