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

`(y^(2))/(a^(2)) - (x^(2))/(b^(2)) =1`
The asymptotes have the equations

`y= \pm (a)/(b) x`

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

The asymptotes are

`y = \pm (5)/(6) x`
Therefore

`(a)/(b) = (10)/(b) = (5)/(6) \\\\ 5b = 60 \\\\ b =12`

Answer:
The equation of the parabola is

`(y^(2))/(100) - (x^(2))/(144) =1`