document.write( "Question 1205247: 1.Find the equation of the circle that passes through the points (0,0), (5,0), and (3,3). Use both geometric and algebraic solution for comparison.\r
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Algebra.Com's Answer #841921 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Ikleyn did the parabola problem for you.  I'll do the circle problem.

1.Find the equation of the circle that passes through the points (0,0), (5,0),
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OK, I'll try to show the straight-edge and compass geometric method to draw\r\n" );
document.write( "a circle through three points.\r\n" );
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document.write( "The geometric method is to find the center by:\r\n" );
document.write( "1. drawing two chords,\r\n" );
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document.write( "2. drawing their perpendicular bisectors (in green):\r\n" );
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document.write( "3. the center is where those two perpendicular bisectors of 2 chords intersect.\r\n" );
document.write( "   (it looks like the point , but we aren't sure\r\n" );
document.write( "of it being exactly that with the geometric method.) \r\n" );
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document.write( "4. Put the foot of the compass on the point where the perpendicular bisectors\r\n" );
document.write( "   of the two chords intersect.  The open your compass to one of the points on\r\n" );
document.write( "   the circle.  Then swing it around and draw a circle. \r\n" );
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document.write( "That's the geometric way to draw a circle through three points.\r\n" );
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document.write( "But the algebraic way is to begin with the general equation \r\n" );
document.write( "or the standard equation for a circle:'\r\n" );
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document.write( "It might be easier to substitute the three points in the standard equation:\r\n" );
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document.write( "Subtract the 1st equation from the other two equations:\r\n" );
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document.write( "Solve the 2nd equation for h\r\n" );
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document.write( "Substitute 5/2 for h in the 3rd equation\r\n" );
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document.write( "Multiply the 3rd equation by 2\r\n" );
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document.write( "Substitute h=5/2, k=1/2 in the 1st equation:\r\n" );
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document.write( "So the standard form is\r\n" );
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document.write( "So now we see that the center = (h,k) = \r\n" );
document.write( "and the radius is \r\n" );
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document.write( "So we graph the circle\r\n" );
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document.write( "Other times we might just want the general equation\r\n" );
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document.write( "Substitute the three points in:\r\n" );
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document.write( "Substitute c=0 in the other two equations:\r\n" );
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document.write( "Divide the 2nd equation by 5 and the third by 3\r\n" );
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document.write( "Solve the 2nd equation for 'a'\r\n" );
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document.write( "Substitute a = -5 in the third equation:\r\n" );
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document.write( "Solve the 3rd equation for b\r\n" );
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document.write( "Substitute in the general solution:\r\n" );
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document.write( "But the trouble with the general equation of a circle is that we can't tell \r\n" );
document.write( "the center and radius from it unless we complete the square and get it into\r\n" );
document.write( "the standard form.\r\n" );
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document.write( "The general form  and the standard form \r\n" );
document.write( "are equivalent.\r\n" );
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document.write( "Edwin

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