Find an equation for the hyperbola that has its center at th

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions. Foci F(0, plusminus 3); vertices V(0, plusminus 2) Give your answer in the form (x - h)^2/a^2 - (y - k)^2/b^2 = 1.

Solution

focii(0,+-3)                Vertices (0,+-2)

This hyperbola is of the form

(y-k)²/a² - (x-h)²/b²=1

Vertices (h,k+-a)    and focii (h,k+-c)

h and k are 0 here

Therefore a=2           and c=3

c²=a²+b²

b²= 5

Therefore the required equation of hyperbola is

y²/4 - x²/5 = 1