Convert the polar equation r = -6 \cos θ to a rectangular equation in x an

Convert the polar equation $r=-6\mathrm{cos}\theta$ to a rectangular equation in x and y.

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Step 1
Consider the given polar equation:

$r=-6\mathrm{cos}\theta$​​​​​​​

Here, the objective is to convert the given polar equation into a rectangular equation in x and y.

Step 2

Re-write the given polar equation as:

$r=-6\mathrm{cos}\theta$

Multiply both sides by r

${r}^{2}=-6r\mathrm{cos}0$

To convert the polar equation into a rectangular equation in x and y, use

${r}^{2}={x}^{2}+{y}^{2}$

$x=r\mathrm{cos}0$

$y=r\mathrm{sin}0$

So

${x}^{2}+{y}^{2}=-6x$

${x}^{2}+{y}^{2}-6x=0$