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

Question

Find an equation in standard form for the hyperbola that satisfies the given conditions:
Transverse axis endpoints (3,3) and (3,−1), conjugate axis length 8

Answer 1

Then easiest way to find the equation for a hyperbola is to graph the information. The distance between the transverse axis endpoints is 4. 2a = the length of the transverse axis. So, 2a = 4, a = 2.

a = the distance between the center and the vertex. So, the center is (3,1).

2b = 8, b = 4

 

c = the distance between the center and the focus

c² = a² + b²

c² = 4 + 16

c² = 20

c = 2√5 ≈ 4.5

 

F(3,5.5) F₁(3-3.5)

 

(y-k)²/a² - (x-h)²/b² = 1

 

(y-1)²/1 - (x-3)²/16 = 1