How do you convert the rectangular equation ${(y - 2)}^{2} + x^{2} = 4$ $(y-2)^2+x^2=4$ into polar form?

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How do you convert the rectangular equation ${(y - 2)}^{2} + x^{2} = 4$ $(y-2)^2+x^2=4$ into polar form?

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Answer 1 · 2017-01-16T20:37:19

Expand the square
Substitute $r^{2}$ $r^2$ for $x^{2} + y^{2}$ $x^2 + y^2$ and $r sin (θ)$ $rsin(theta)$ for y
Combine like terms
Divide both sides by r
Express r in terms of $θ$ $theta$

Explanation:

Expand the square:

$y^{2} - 4 y + 4 + x^{2} = 4$ $y^2 -4y + 4 + x^2 = 4$

Substitute $r^{2}$ $r^2$ for $x^{2} + y^{2}$ $x^2 + y^2$ and $r cos (θ)$ $rcos(theta)$ for y:

$r^{2} - 4 r sin (θ) + 4 = 4$ $r^2 -4rsin(theta) + 4 = 4$

Combine like terms:

$r^{2} - 4 r sin (θ) = 0$ $r^2 -4rsin(theta) = 0$

Divided both sides by r:

$r - 4 sin (θ) = 0$ $r -4sin(theta) = 0$

Express r in terms of theta:

$r = 4 sin (θ)$ $r = 4sin(theta)$

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How do you convert the rectangular equation ${(y - 2)}^{2} + x^{2} = 4$ $(y-2)^2+x^2=4$ into polar form?

1 Answer

Explanation:

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How do you convert the rectangular equation (y-2)^2+x^2=4(y−2)2+x2=4(y-2)^2+x^2=4 into polar form?

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How do you convert the rectangular equation ${(y - 2)}^{2} + x^{2} = 4$ $(y-2)^2+x^2=4$ into polar form?