Find an equation in standard form for the hyperbola that satisfies the given conditions. Foci (0,±15)​, transverse axis length

Question

Find an equation in standard form for the hyperbola that satisfies the given conditions.

Foci (0,±15)​, transverse axis length (Type an equation. Type your answer in standard​ form.)

Answer 1

c^2=a^2+b^2

y^2/a^2 -x^2/b^2 =1 for vertical transverse axis

foci =(0, +/-c) = (0,15), (0,-15) center = (0,0)

(0,a) and (0,-a) = (0, 12), (0,-12) are the vertices

a=12, b=9, c=15

12^2+9^2

=144+81

=225

=15^2

y^2/12^2 -x^2/9^2 = 1

or

y^2/144 - x^2/81 = 1

(y/12)^2 - (x/9)^2 =1

or

81y^2 - 144x^2 =81(144)= 11,664