Question

Write the equation of a hyperbola with foci at (3, -3) and (3, 7) and vertices at (3, -1) and (3, 5).

Answer 1

Answer:

The answer to your question is

                           $\frac{(y - k)^{2}}{9} - \frac{(x - h)^{2} }{16} = 1$

Step-by-step explanation:

See the picture below

- From the picture we conclude that it is a vertical hyperbola

Center = (3, 2)

c = 5

a = 3             b² = c² - a²        b² = 5² - 3²    b² = 25 - 9    b² = 16

b = 4

- Equation

                     $\frac{(y - k)^{2}}{a^{2} } - \frac{(x - h)^{2} }{b^{2}} = 1$

- Substitution

                    $\frac{(y - 2)^{2}}{3^{2} } - \frac{(x - 3)^{2}}{4^{2}} = 1$                      

- Result

                   $\frac{(y - k)^{2}}{9} - \frac{(x - h)^{2} }{16} = 1$