hyperbola help

Question

Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y = ±x.

Answer 1

The vertices of hyperbola is (0, 8) and (0, -8) and asymptote y = ± (4/3)x.

The standard form of equation of hyperbola with center at the origin (where a and b are not equals to 0) is x ²/a ² - y ²/b ² = 1 (Transverse axis is horizontal) or y ²/a ²- x ²/b ² = 1 (Transverse axis is vertical).

The y - coordinates of the  vertices points are 8 and - 8.

The value of a = 8 because the vertices are eight units from the center.

The asymptote y = ± (4/3)x is comparison with y = ± (a/b) x.

a/b = 4/3

8/b = 4/3.

4b = 24

b = 6

The standard form of the hyperbola equation is y ²/8 ² - x ²/6 ² = 1.