# Convert the polar equation to a rectangular equation. r = -9 cos theta

heelallev5 2022-08-05 Answered
Convert the polar equation to a rectangular equation.
$r=-9\mathrm{cos}\theta$
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## Answers (2)

Nicole Soto
Answered 2022-08-06 Author has 10 answers
$r=\sqrt{{x}^{2}+{y}^{2}}$ and $x=r\mathrm{cos}\theta ⇒\mathrm{cos}\theta =\frac{x}{r}$
$\therefore r=-9\mathrm{cos}\theta =-9\ast \frac{x}{r}$
${r}^{2}=-9x$
$⇒{x}^{2}+{y}^{2}=-9x$
$⇒\left(x+\frac{9}{2}{\right)}^{2}+{y}^{2}=\frac{81}{4}←$ Completing the square
$⇒\frac{\left(x+\frac{9}{2}{\right)}^{2}}{\left(\frac{9}{2}{\right)}^{2}}+\frac{{y}^{2}}{\left(\frac{9}{2}{\right)}^{2}}=1←$ Equation of an ellipse
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ghettoking6q
Answered 2022-08-07 Author has 8 answers
Given the polar equation
$r=-9\mathrm{cos}\theta$
Multiply both sides of the equation by r.
${r}^{2}=-9\mathrm{cos}\theta$
Use the following conversions: ${r}^{2}={x}^{2}+{y}^{2},x=r\mathrm{cos}\theta$.
${x}^{2}+{y}^{2}=-9x$
Add 9x to both sides of the equation.
$\left({x}^{2}+9x\right)+{y}^{2}=0$
Complete the square.
$\left({x}^{2}+9x\frac{81}{4}\right)+{y}^{2}=\frac{81}{4}$
$\left(x+\frac{9}{2}{\right)}^{2}+{y}^{2}=\frac{81}{4}$....Rectangular Equation
Conic Section is a Circle
center: (h, k)------(-9/2, 0)
radius (r): 9/2
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