wrte the standard form equation for a hyperbola with a center (0,0) a vertex at (0,3) and a focus at (0,5)?

Answer 1

The distance from the center to a vertex is a.

a = 3 - 0 = 3
a² = 9

The distance from the center to a focus is c.

c = 5 - 0 = 5
c² = 25

b² = c² - a² = 25 - 9 = 16

Since the center, vertex, and focus are in a vertical line, the hyperbolas open vertically.

The equation of the hyperbolas is:

y²/a² - x²/b² = 1
y²/9 - x²/16 = 1