Question

Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ± five divided by six times x.. (2 points)

Answer 1

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
$\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} =1$
The asymptotes have the equations
$y= \pm \frac{a}{b} x$

For the given problem,
The vertices are located at (0, +/-10).
Therefore a = 10.

The asymptotes are
$y = \pm \frac{5}{6} x$
Therefore
$\frac{a}{b} = \frac{10}{b} = \frac{5}{6} \\\\ 5b = 60 \\\\ b =12$

Answer:
The equation of the parabola is
$\frac{y^{2}}{100} - \frac{x^{2}}{144} =1$