document.write( "Question 1049883: the center of a circle is (x,3x). Find x if the circle passes
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Algebra.Com's Answer #665443 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Since x is a variable, and the center of a circle is a constant, to\r\n" );
document.write( "avoid a conflict of letters, I will change the problem so that the \r\n" );
document.write( "center is (c,3c) and not (x,3x).  So consider the problem as:\r\n" );
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\n" ); document.write( "the center of a circle is (c,3c). Find c if the circle passes through
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document.write( "The equation of any circle is \r\n" );
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document.write( "where the center is (h,k) and the radius is r.\r\n" );
document.write( "So (h,k) = (c,3c) and r=5 units (because the diameter \r\n" );
document.write( "is 10 units and the radius is one-half the diameter).\r\n" );
document.write( "Plugging in:\r\n" );
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document.write( "Since it passes through the origin, we can\r\n" );
document.write( "substitute (x,y) = (0,0). Plugging in:\r\n" );
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document.write( "There are two answers.   Notice that both circles pass through\r\n" );
document.write( "the origin and both are 10 units across, that is, the diameter\r\n" );
document.write( "is 10 units, as you can see by the green diameters below:\r\n" );
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document.write( "So there are two solutions, \r\n" );
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document.write( " and \r\n" );
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document.write( "You should point out to your teacher that there is a conflict \r\n" );
document.write( "of letters.  x cannot represent a variable if it is supposed \r\n" );
document.write( "to represent a constant.\r\n" );
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document.write( "Edwin

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