document.write( "Question 1039812: Determine a polar equation for the circle with a radius
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Algebra.Com's Answer #654581 by Edwin McCravy(20055)\"\" \"About 
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First we get the rectangular equation of the circle.\r\n" );
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document.write( "The center is the polar point, which is\r\n" );
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document.write( "\"%28matrix%281%2C3%2C1%2C%22%2C%22%2Cpi%2F2%29%29\"\r\n" );
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document.write( "That's the point that we get when we \r\n" );
document.write( "1. swing counter-clockwise \"pi%2F2\" radians or 90° \r\n" );
document.write( "   from the right side of the x-axis, and\r\n" );
document.write( "2. Go out 1 unit in that direction, which\r\n" );
document.write( "   turns out to be directly upward.\r\n" );
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document.write( "So that's the same point as the rectangular point (0,1)\r\n" );
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document.write( "So the circle with that center and a radius of \"sqrt%285%29\" is this\r\n" );
document.write( "black circle:\r\n" );
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document.write( "which has rectangular equation:\r\n" );
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document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\" which becomes\r\n" );
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document.write( "\"%28x-0%29%5E2%2B%28y-1%29%5E2=%28sqrt%285%29%29%5E2\" or\r\n" );
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document.write( "\"x%5E2%2B%28y-1%29%5E2=5\"\r\n" );
document.write( "\"x%5E2%2B%28y%5E2-2y%2B1%29=5\"\r\n" );
document.write( "\"x%5E2%2By%5E2-2y%2B1=5\"\r\n" );
document.write( "\"x%5E2%2By%5E2-2y=4\"\r\n" );
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document.write( "Then to change from rectangular to polar or\r\n" );
document.write( "vice-versa we draw this:\r\n" );
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document.write( "From which we see that \r\n" );
document.write( "\"x%2Fr=cos%28theta%29\", \"y%2Fr=sin%28theta%29\", and \"x%5E2%2By%5E2=r%5E2\"\r\n" );
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document.write( "So we replace the x2+y2 by r2 and\r\n" );
document.write( "the y using \"y%2Fr=sin%28theta%29\" solved for y, \"y=r%2Asin%28theta%29\"\r\n" );
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document.write( "So the rectangular equation \"x%5E2%2By%5E2-2y=4\" becomes\r\n" );
document.write( "the polar equation:\r\n" );
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document.write( "\"r%5E2-2r%2Asin%28theta%29=4\"\r\n" );
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document.write( "Edwin
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