Question

guided practice
now find the foci of the graph $\frac{x^2}{4} - \frac{y^2}{9} = 1$ by answering a few questions.
type your answer and then click or tap done.
what are the values of $a^2$ and $b^2$?
$a^2 = (\quad)$ and $b^2 = (\quad)$

Explanation:

Step1: Compare with hyperbola standard form

The standard form of a horizontal transverse axis hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.

Step2: Match given equation terms

Given $\frac{x^2}{4} - \frac{y^2}{9} = 1$, so $\frac{x^2}{a^2}=\frac{x^2}{4}$ and $\frac{y^2}{b^2}=\frac{y^2}{9}$.

Step3: Identify $a^2$ and $b^2$

By direct matching, $a^2=4$ and $b^2=9$.

Answer:

$a^2 = 4$ and $b^2 = 9$