# How do you write the equation of the hyperbola given Foci: (-8,0),(80) and vertices (-7,0), (7,0)?

Nov 11, 2016

The equation of the ellipse is ${x}^{2} / 49 - {y}^{2} / 15 = 1$

#### Explanation:

The center is $= \left(0 , 0\right)$
The vertices are $= \left(\pm a , 0\right) = \left(\pm 7 , 0\right)$
The foci are $= \pm c , 0$
Therefore, ${c}^{2} = {a}^{2} + {b}^{2}$
So, ${b}^{2} = {c}^{2} - {a}^{2} = 64 - 49 = 15$

The equation of the hyperbola is
${x}^{2} / {a}^{2} - {y}^{2} / {b}^{2} = 1$

${x}^{2} / 49 - {y}^{2} / 15 = 1$
graph{x^2/49-y^2/15=1 [-16.02, 16.02, -8.01, 8.02]}