Find the standard form of the equation of the hyperbola sati

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at (0, -2) and (0, 2); vertices at (0, 1) and (0, -1)

Solution

vertices are symmertic about origin => center of hyperbola is at origin

also vertices lie on y-axis so

y²/a² - x²/b² = 1

a = 1

and a² + b² = 2²

b² = 3

=> y² - x²/3 = 1