How do you convert $- 3 y = 7 x^{2} - 2 x y$ $-3y= 7x^2-2xy$ into a polar equation?

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How do you convert $- 3 y = 7 x^{2} - 2 x y$ $-3y= 7x^2-2xy$ into a polar equation?

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Answer 1 · 2016-10-19T20:13:18

$r = \frac{3 sin θ}{sin 2 θ - 7 {cos}^{2} θ}$ $r=(3sintheta)/(sin2theta-7cos^2theta$

Explanation:

Use the substitution $x = r cos θ$ $x=rcostheta$ and $y = r sin θ$ $y=rsintheta$
then we have
$- 3 r sin θ = 7 r^{2} {cos}^{2} θ - 2 r^{2} sin θ cos θ$ $-3rsintheta=7r^2cos^2theta-2r^2sinthetacostheta$
divding by r and $sin 2 θ = 2 sin θ cos θ$ $sin2theta=2sinthetacostheta$
$- 3 sin θ = r (7 {cos}^{2} θ - sin 2 θ)$ $-3sintheta=r(7cos^2theta-sin2theta)$
$r = - \frac{3 sin θ}{7 {cos}^{2} θ - sin 2 θ} = \frac{3 sin θ}{sin 2 θ - 7 {cos}^{2} θ}$ $r=-(3sintheta)/(7cos^2theta-sin2theta)=(3sintheta)/(sin2theta-7cos^2theta)$

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How do you convert $- 3 y = 7 x^{2} - 2 x y$ $-3y= 7x^2-2xy$ into a polar equation?

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How do you convert -3y= 7x^2-2xy −3y=7x2−2xy-3y= 7x^2-2xy into a polar equation?

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How do you convert $- 3 y = 7 x^{2} - 2 x y$ $-3y= 7x^2-2xy$ into a polar equation?