# How do you graph x^2-4(y+6)^2 = 9?

Dec 21, 2016

$\textcolor{p u r p \le}{\text{Note that graphing and sketching are two different things}}$
$\textcolor{p u r p \le}{\text{To sketch a curve you have to mathematically determine important points}}$
Depends on what medium you use to plot it. A bit of specialist software could do so by entering the equation as presented.

However, if you wish to do this by hand from a table of values you need to manipulate the equation to give you the format of $y = \text{something}$
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$4 {\left(y + 6\right)}^{2} = {x}^{2} - 9$

${\left(y + 6\right)}^{2} = \frac{1}{4} {x}^{2} - \frac{9}{4}$

$y + 6 = \pm \frac{\sqrt{{x}^{2} - 9}}{2}$

$y = \pm \frac{\sqrt{{x}^{2} - 9}}{2} - 6$
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$\textcolor{red}{\text{Split equation} \to y = \pm \frac{\sqrt{{x}^{2} - 9}}{2} - 6}$

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$\textcolor{red}{\text{Full equation} \to {x}^{2} - 4 {\left(y + 6\right)}^{2} = 9}$