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What is the center of the hyperbola $9x^2 - y^2 = 81$ ? $\newline$ $(\_,\_)$

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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

9x^2 - y^2 = 81

?

\newline

(\_,\_)

Identify Equation: Identify the equation of the hyperbola. $\newline$ The given equation is $9x^2 - y^2 = 81$ .
Rewrite Equation: Rewrite the equation in standard form. $\newline$ To do this, we need to isolate the terms with variables on one side and the constant on the other side. Since the equation is already in this form, we can proceed to the next step.
Divide by Constant: Divide the equation by the constant term to get the standard form of the hyperbola equation. $\newline$ Divide both sides of the equation by $81$ to get $\frac{9x^2}{81} - \frac{y^2}{81} = \frac{81}{81}$ . $\newline$ Simplify to get $\frac{x^2}{9} - \frac{y^2}{81} = 1$ .
Identify Center: Identify the center of the hyperbola. The standard form of a hyperbola is $(x-h)^2/a^2 - (y-k)^2/b^2 = 1$ , where $(h, k)$ is the center of the hyperbola. In our equation $x^2/9 - y^2/81 = 1$ , we can see that $h = 0$ and $k = 0$ , so the center is at the origin $(0, 0)$ .

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