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

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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

=

100

?

\newline

(\_,\_)

Rewrite Equation in Standard Form: The equation of the hyperbola is given by $x^2 - y^2 = 100$ . To find the center, we need to express the equation in its standard form.
Standard Form of Hyperbola: The standard form of a hyperbola is $(x - h)^2/a^2 - (y - k)^2/b^2 = 1$ for a horizontal hyperbola, or $(y - k)^2/a^2 - (x - h)^2/b^2 = 1$ for a vertical hyperbola, where $(h, k)$ is the center of the hyperbola.
Divide by $100$ : The given equation $x^2 - y^2 = 100$ can be rewritten as $\frac{x^2}{100} - \frac{y^2}{100} = 1$ by dividing both sides by $100$ .
Identify Center Coordinates: Now, the equation $\frac{x^2}{100} - \frac{y^2}{100} = 1$ is in the standard form of a hyperbola, where $a^2 = 100$ and $b^2 = 100$ . Since there is no $(x - h)$ or $(y - k)$ term, it implies that $h = 0$ and $k = 0$ .
Identify Center Coordinates: Now, the equation $\frac{x^2}{100} - \frac{y^2}{100} = 1$ is in the standard form of a hyperbola, where $a^2 = 100$ and $b^2 = 100$ . Since there is no $(x - h)$ or $(y - k)$ term, it implies that $h = 0$ and $k = 0$ .Therefore, the center of the hyperbola is at the point $(h, k)$ , which is $(0, 0)$ .

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