Hyperbolas question on constant difference

Question

Identify the constant difference for a hyperbola with foci (0, −5) and (0, 5) and a point on the hyperbola (0, 3).

Answer 1

from the two foci, (0,5), (0,-5), in the middle (0,0) will be the center, then c=5, the point (0,3) is on the hyperbola which is also on the major axis, so a=3, then a²+b²=c^2, b should be 4, the hyperbola equation should be

y²/9-x²/16=1

the constant difference=2a=6