find equatio of the hyperbola?

Question

Find an equation for the hyperbola which has a vertex at (3,7), a focus at (3,-1) and its center is (3,5)

Answer 1

Find an equation for the hyperbola which has a vertex at (3,7), a focus at (3,-1) and its center is (3,5).

The center (h,k) = (3,5).

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

The distance from the center to the vertex is a.

a = |7 - 5| = 2
a² = 4

The distance from the center to the focus is c.

c = |-1 - 5| = 6
c² = 36

b² = c² - a² = 36 - 4 = 32

The equation of the hyperbola can now be written.

(y - k)²/a² - (x - h)²/b² = 1

(y - 5)²/4 - (x - 3)²/32 = 1