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What is the center of the hyperbola $x^2 - 25y^2 - 100 = 0$ ? $\newline$ $(\_,\_)$

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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 - 25y^2 - 100 = 0

?

\newline

(\_,\_)

Move constant term: $x^2 - 25y^2 - 100 = 0$ $\newline$ Move the constant term to the right side. $\newline$ $x^2 - 25y^2 = 100$
Convert to standard form: $x^2 - 25y^2 = 100$ $\newline$ Convert the equation into standard form. $\newline$ Divide both sides of the equation by $100$ . $\newline$ $\frac{x^2}{100} - \frac{25y^2}{100} = \frac{100}{100}$ $\newline$ $\frac{x^2}{100} - \frac{y^2}{4} = 1$
Find center of hyperbola: $\frac{x^2}{100} - \frac{y^2}{4} = 1$ $\newline$ Find the center of the hyperbola. $\newline$ The standard form of a hyperbola is $\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$ , where $(h, k)$ is the center. $\newline$ Here, the equation can be written as $\frac{(x - 0)^2}{100} - \frac{(y - 0)^2}{4} = 1$ . $\newline$ Thus, $h = 0$ and $k = 0$ . $\newline$ Center of the hyperbola: $(0, 0)$

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