Question

guided practice what are the foci of the graph \\(\frac{x^2}{24} - y^2 = 1\\)? a. (±25, 0) b. (±√24, 0) c. (±1, 0) d. (±5, 0)

Explanation:

Step1: Identify hyperbola standard form

The given equation $\frac{x^2}{24} - y^2 = 1$ matches the horizontal hyperbola form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.

Step2: Find $a^2$ and $b^2$

$a^2=24$, $b^2=1$

Step3: Calculate $c$ using $c^2=a^2+b^2$

$c^2=24+1=25$, so $c=\sqrt{25}=5$

Step4: State foci coordinates

For horizontal hyperbola, foci are $(\pm c,0)=(\pm5,0)$

Answer:

D. $(\pm5,0)$