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What is the center of the hyperbola $4x^2 - y^2 - 36 = 0$ ? $\newline$ $(\_,\_)$

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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

4x^2 - y^2 - 36 = 0

?

\newline

(\_,\_)

Move constant term: $4x^2 - y^2 - 36 = 0$ $\newline$ Move the constant term to the right side of the equation. $\newline$ $4x^2 - y^2 = 36$
Convert to standard form: $4x^2 - y^2 = 36$ $\newline$ Convert the equation into standard form by dividing both sides by $36$ . $\newline$ $\frac{4x^2}{36} - \frac{y^2}{36} = \frac{36}{36}$ $\newline$ Simplify the fractions. $\newline$ $\frac{x^2}{9} - \frac{y^2}{36} = 1$
Simplify fractions: $\frac{x^2}{9} - \frac{y^2}{36} = 1$ $\newline$ Identify the center of the hyperbola. $\newline$ The equation is now in the standard form $(x - h)^2/a^2 - (y - k)^2/b^2 = 1$ , where $h$ and $k$ are the $x$ and $y$ coordinates of the center, respectively. Since there are no $(x - h)$ or $(y - k)$ terms, $h$ and $k$ are both $(x - h)^2/a^2 - (y - k)^2/b^2 = 1$ $0$ . $\newline$ Center of the hyperbola: $(x - h)^2/a^2 - (y - k)^2/b^2 = 1$ $1$

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