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

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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

x^2 - y^2 = 36

?

\newline

(\_,\_)

Write Equation: Write the given equation of the hyperbola. $\newline$ The given equation is $x^2 - y^2 = 36$ .
Standard Form: Rewrite the equation in standard form. $\newline$ To get the standard form of the hyperbola equation, we need to isolate the terms with $x$ and $y$ on one side and the constant on the other side. The equation is already in this form, so we can proceed to the next step.
Divide by $36$ : Divide both sides of the equation by $36$ to get the standard form of the hyperbola equation. $\newline$ $\frac{x^2}{36} - \frac{y^2}{36} = \frac{36}{36}$ $\newline$ Simplify the equation to get: $\newline$ $\frac{x^2}{36} - \frac{y^2}{36} = 1$
Identify Center: Identify the center of the hyperbola. The standard form of the hyperbola equation is $(x-h)^2/a^2 - (y-k)^2/b^2 = 1$ , where $(h, k)$ is the center of the hyperbola. In our equation, $x^2/36 - y^2/36 = 1$ , we can see that $h = 0$ and $k = 0$ , so the center is at the origin $(0, 0)$ .

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