Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ±1 divided by 3*x

Question

PRE CALC HELP

Answer 1

THIS HYPERBOLA HAS VERTICAL TRANSVERSE AXIS with vertices on y axis at -4 and 4 and so it's centered at the origin.

Therefore a = 4.

Asymptotes have linear equations y = ±(a/b)x and (a/b) = 1/3 (given).

Therefore 9a² = b² so b² = 9(4²) = 144.

 

The equation is y²/a² - x²/b² = 1  and all you need to do is to substitute for those denominators now.