How do you convert $y = 3 x^{2} - 2 x + 4 x y^{2}$ $y= 3x^2 -2x+4xy^2$ into a polar equation?

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How do you convert $y = 3 x^{2} - 2 x + 4 x y^{2}$ $y= 3x^2 -2x+4xy^2$ into a polar equation?

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Answer 1 · 2018-01-19T10:04:47

$4 r^{2} cos θ {sin}^{2} θ + 3 r {cos}^{2} θ - (2 cos θ + sin θ) = 0$ $4r^2costhetasin^2theta+3rcos^2theta-(2costheta+sintheta)=0$

Explanation:

The relation between polar coordiates $(r, θ)$ $(r,theta)$ and Cartesian corrdinates $(x, y)$ $(x,y)$ is given by $x = r cos θ$ $x=rcostheta$ and $y = r sin θ$ $y=rsintheta$

Hence we can write $y = 3 x^{2} - 2 x + 4 x y^{2}$ $y=3x^2-2x+4xy^2$ as

$r sin θ = 3 r^{2} {cos}^{2} θ - 2 r cos θ + 4 r^{3} cos θ {sin}^{2} θ$ $rsintheta=3r^2cos^2theta-2rcostheta+4r^3costhetasin^2theta$

or $4 r^{2} cos θ {sin}^{2} θ + 3 r {cos}^{2} θ - (2 cos θ + sin θ) = 0$ $4r^2costhetasin^2theta+3rcos^2theta-(2costheta+sintheta)=0$

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How do you convert $y = 3 x^{2} - 2 x + 4 x y^{2}$ $y= 3x^2 -2x+4xy^2$ into a polar equation?

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Explanation:

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How do you convert y= 3x^2 -2x+4xy^2 y=3x2−2x+4xy2y= 3x^2 -2x+4xy^2 into a polar equation?

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How do you convert $y = 3 x^{2} - 2 x + 4 x y^{2}$ $y= 3x^2 -2x+4xy^2$ into a polar equation?