How do you convert $r = \frac{100}{3 - 2 cos θ}$ $r=100/(3-2costheta)$ into cartesian form?

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Answer 1 · 2016-08-17T15:13:40

$2491 x^{2} - 9 y^{2} - 10000 x + 10000 = 0$ $2491x^2-9y^2-10000x+10000=0$

The given polar equation is in the form

$\frac{a (1 - e^{2})}{r} = 1 - s cos θ$ $(a(1-e^2))/r=1-scos theta$ that represents an ellipse with

eccentricity $e = \frac{2}{3}$ $e=2/3$ ans semi major axis a = 60..

Use the conversion formula

$r (cos θ, sin θ) = (x, y)$ $r(cos theta, sin theta)=(x, y)$ that gives

$r = \sqrt{x^{2} + y^{2}} and cos θ = \frac{x}{r}$ $r =sqrt(x^2+y^2) and cos theta = x/r$ .

Substituting and rearranging,

$3 (\sqrt{x^{2} + y^{2}}) = 50 (2 - x)$ $3(sqrt(x^2+y^2))=50(2-x)$ . Squaring and rearranging,

, $2491 x^{2} - 9 y^{2} - 10000 x + 10000 = 0$ $2491x^2-9y^2-10000x+10000=0$

How do you convert r=100/(3-2costheta)r=1003−2cosθr=100/(3-2costheta) into cartesian form?