How do you convert $x^2 + y^2 = 4y$ into polar form?

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Answer 1 · 2018-04-15T03:47:29

$color(crimson)(r = 4 sin theta$

$x = r cos theta, y = r sin theta$

Given : $x^2 + y^2 = 4y$

Substituting for x & y in terms of r and theta,

$r^2 cos^2 theta + r^2 sin^2 theta = 4 r sin theta$

$r^2 (cos^2 theta + sin^2 theta) = 4 r sin theta$

$r^2 = 4 r sin theta, " as " cos^2 theta + sin^2 theta = 1$

$color(crimson)(r = 4 sin theta$

How do you convert x^2 + y^2 = 4yx^2 + y^2 = 4y into polar form?