# How do you write the equation of the hyperbola given Foci: (-sqrt34,0),(sqrt34,0) and vertices (-5,0), (5,0)?

Oct 28, 2016

The equation of the hyperbola is ${x}^{2} / 25 - {y}^{2} / 9 = 1$

#### Explanation:

The equation of a hyperbola is ${\left(x - h\right)}^{2} / {a}^{2} - {\left(y - k\right)}^{2} / {b}^{2} = 1$

This a left to right hyperbola
The center is $\left(0 , 0\right)$ that is $h = k = 0$
Therefore $a = 5$
And as the foci are $\left(h \pm c , k\right) = \pm \sqrt{34} , 0$
So $c = \sqrt{{a}^{2} + {b}^{2}}$

Therefore, ${c}^{2} = {a}^{2} + {b}^{2}$
${b}^{2} = {c}^{2} - {a}^{2} = 34 - 25 = 9$
So $b = 3$
So the equation of the hyperbola is ${x}^{2} / 25 - {y}^{2} / 9 = 1$

graph{x^2/25-y^2/9=1 [-20, 20, -10, 10]}