What is the polar form of $x^{2} + y^{2} = 2 x$ $x^2 + y^2 = 2x$ ?

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Answer 1 · 2014-11-12T20:34:09

$x^{2} + y^{2} = 2 x$ $x^2+y^2=2x$ , which looks like:

enter image source here

by plugging in ${(x=rcos theta),(y=rsin theta):}$ ,

$=> (rcos theta)^2+(r sin theta)^2=2rcos theta$

by multiplying out,

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

by factoring out $r^2$ from the left-hand side,

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

by $cos^2theta+sin^2theta=1$ ,

$=> r^2=2rcos theta$

by dividing by $r$ ,

$=> r=2cos theta$ , which looks like:

enter image source here

As you can see above, $x^2+y^2=2x$ and $r=2cos theta$ give us the same graphs.

I hope that this was helpful.

What is the polar form of x^2 + y^2 = 2xx2+y2=2x x^2 + y^2 = 2x?