# What is the equation of a hyperbola with a = 3 and c = 7? Assume that the transverse axis is horizontal.

Mar 24, 2017

The standard equation of hyperbola with a horizontal transverse axis is:

${\left(x - h\right)}^{2} / {a}^{2} - {\left(y - k\right)}^{2} / {b}^{2} = 1$ and $c = \sqrt{{a}^{2} + {b}^{2}}$

#### Explanation:

Use the equation $c = \sqrt{{a}^{2} + {b}^{2}}$ to find the value of b:

$7 = \sqrt{{3}^{2} + {b}^{2}}$

$49 = 9 + {b}^{2}$

${b}^{2} = 40$

$b = \sqrt{40}$

Assume that the center of hyperbola is $\left(0 , 0\right)$

${\left(x - 0\right)}^{2} / {3}^{2} - {\left(y - 0\right)}^{2} / {\left(\sqrt{40}\right)}^{2} = 1$