# How do you write the equation of the hyperbola given Foci: (0,-7),(0,7) and vertices (0,-3), (0,3)?

Dec 13, 2016

The equation is ${y}^{2} / 9 - {x}^{2} / 40 = 1$

#### Explanation:

The foci are $F = \left(0 , 7\right)$ and $F ' = \left(0 , - 7\right)$

The vertices are $A = \left(0 , 3\right)$ and $A ' = \left(0 , - 3\right)$

So, the center is $C = \left(0 , 0\right)$

So, $a = 3$

$c = 7$

and $b = \sqrt{{c}^{2} - {a}^{2}} = \sqrt{49 - 9} = \sqrt{40}$

Therefore, the equation of the hyperbola is

${y}^{2} / {a}^{2} - {x}^{2} / {b}^{2} = 1$

${y}^{2} / 9 - {x}^{2} / 40 = 1$

graph{(y^2/9-x^2/40-1)=0 [-11.25, 11.25, -5.625, 5.625]}