The hyperbola has vertices: ( 0, +/- 6 ). It means that a = 6 ( semi-minor axis ). Also, asymptotes are: y = +/- 3/4 x The formula is: y = +/- b/ a x So: 3/4 = b/a b/6 = 3/4 4 b = 6 * 3 4 b = 18 b = 18 : 4 b = 9/2 The equation of the hyperbola is: x² / a² - y² / b² = 1 x² / 36 - y² / (9/2)² = 1 Answer: x² / 36 - 4y² / 81 = 1
