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What is the center of the hyperbola $4x^2 - y^2 = 36$ ? $\newline$ $(\_,\_)$

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Find properties of hyperbolas from equations in general form

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Q. What is the center of the hyperbola

4x^2 - y^2 = 36

?

\newline

(\_,\_)

Write Equation: Write the given equation of the hyperbola. $\newline$ The given equation is $4x^2 - y^2 = 36$ .
Standard Form: Rewrite the equation in standard form. $\newline$ To find the center, we need to express the equation in the standard form of a hyperbola. For a hyperbola centered at $(h, k)$ , the standard form is $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$ . We can divide both sides of the equation by $36$ to get it into standard form. $\newline$ $\frac{4x^2}{36} - \frac{y^2}{36} = \frac{36}{36}$ $\newline$ $\frac{x^2}{9} - \frac{y^2}{36} = 1$
Identify Center: Identify the center of the hyperbola. $\newline$ From the standard form $\frac{x^2}{9} - \frac{y^2}{36} = 1$ , we can see that the equation can be written as $\left(x-0\right)^2/9 - \left(y-0\right)^2/36 = 1$ . This means that $h = 0$ and $k = 0$ , so the center of the hyperbola is at $(0, 0)$ .

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