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Write the equation in standard form for the hyperbola $9y^2 - x^2 = 36$ . $\newline$ ______

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Convert equations of hyperbolas from general to standard form

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Q. Write the equation in standard form for the hyperbola

9y^2 - x^2 = 36

.

\newline

______

Identify Operation: Identify the operation to write the equation in standard form. $\newline$ Divide both sides by $36$ to isolate the terms involving $x$ and $y$ on one side and the constant on the other side. $\newline$ Operation: Division
Perform Division: Perform the division operation on the equation $9y^2 - x^2 = 36$ . Divide each term by $36$ : $(9y^2)/36 - (x^2)/36 = 36/36$ Simplify each term: $y^2/4 - x^2/36 = 1$
Rewrite Equation: Rewrite the equation to match the standard form of a hyperbola. $\newline$ The standard form of a hyperbola is $(\frac{y^2}{a^2}) - (\frac{x^2}{b^2}) = 1$ , where $a$ and $b$ are constants. $\newline$ In this case, $a^2 = 4$ and $b^2 = 36$ , so $a = 2$ and $b = 6$ . $\newline$ The standard form of the hyperbola is: $\newline$ $\frac{y^2}{4} - \frac{x^2}{36} = 1$

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