Question

hyperbolas
you are looking for the foci of the graph $\frac{x^2}{4} - \frac{y^2}{9} = 1$. so far, you have determined that $a^2 = 4$ and $b^2 = 9$. use the pythagorean theorem to find the value of $c$.
what is the value of $c$?
a. $pmsqrt{5}$
b. $pm13$
c. $pmsqrt{13}$
d. $pm2$

Explanation:

Step1: Recall hyperbola $c$ formula

$c^2 = a^2 + b^2$

Step2: Substitute given values

$c^2 = 4 + 9$

Step3: Calculate $c^2$ and solve for $c$

$c^2 = 13 \implies c = \pm\sqrt{13}$

Answer:

C. $\pm\sqrt{13}$