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

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Answer 1 · 2016-05-08T17:24:31

$r^2 = r cos theta$

To convert to polar form, substitute:

${ (x = r cos theta), (y = r sin theta) :}$

then simplify:

So:

$x^2+y^2 = x$

becomes:

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

The left hand side simplifies as follows:

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

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

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

$=r^2$

So:

$r^2 = r cos theta$

You might be tempted to simplify this by dividing both sides by $r$ to get:

$r = cos theta$

but that loses the solution $r = 0$ , so it is probably best left in the form:

$r^2 = r cos theta$

How do you convert x^2+y^2=xx^2+y^2=x to polar form?