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What is the center of the hyperbola $(\frac{x^2}{144}) - (\frac{y^2}{81}) = 1$ ? $\newline$ (_,_)

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Find the center of a hyperbola

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Q. What is the center of the hyperbola

(\frac{x^2}{144}) - (\frac{y^2}{81}) = 1

?

\newline

(_____,_____)

Standard Form of Hyperbola: The standard form of a hyperbola centered at $(h, k)$ is either $\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$ for a horizontal hyperbola or $\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1$ for a vertical hyperbola. We need to compare the given equation with the standard form to find the values of $h$ and $k$ , which represent the center of the hyperbola.
Comparing with Standard Form: The given equation is $(\frac{x^2}{144} - \frac{y^2}{81} = 1)$ . We can rewrite this as $(\frac{(x - 0)^2}{144} - \frac{(y - 0)^2}{81} = 1)$ to make it look more like the standard form. From this, we can see that $h = 0$ and $k = 0$ , since there are no terms to shift the $x$ and $y$ values in the equation.
Finding the Center: Since we have found that $h = 0$ and $k = 0$ , the center of the hyperbola is at the point $(0, 0)$ .

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