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Question

# Convert the polar equation to rectangular form.$r^2=4\cos2\theta$

Solution

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Given polar equation:

$r^2=4\cos 2 \theta$

We need to convert the given equation to its rectangular form. That is, we need to rewrite the equation such that it contains the variables $x$ and $y$ instead of the variables $r$ and $\theta$.

Formulas relating polar and rectangular coordinates:

\begin{aligned} x&=r\cos \theta \\ y&=r\sin \theta \\ \\ r^2&=x^2+y^2 \\ \tan \theta&=\frac{y}{x} \end{aligned}

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