Question

guided practice
what are the foci of the graph (\frac{y^2}{64} - \frac{x^2}{36} = 1)?
a. ((0, pm 8))
b. ((0, pm sqrt{28}))
c. ((0, pm 10))
d. ((0, pm 6))

Explanation:

Step1: Identify hyperbola parameters

The given equation is $\frac{y^2}{64} - \frac{x^2}{36} = 1$, which matches the vertical hyperbola form $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$. So $a^2=64$, $b^2=36$.

Step2: Calculate $c$ for foci

Use hyperbola relationship $c^2=a^2+b^2$.
$c^2=64+36=100$, so $c=\sqrt{100}=10$.

Step3: State foci coordinates

For vertical hyperbola, foci are at $(0, \pm c)$, so $(0, \pm10)$.

Answer:

C. (0, ±10)