document.write( "Question 1076714: Find an equation of the circle that passes through the points (2,3), (4,5), and (0,-3). \n" ); document.write( "

Algebra.Com's Answer #691372 by Alan3354(69443) $\"\"$ $\"About$

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Find an equation of the circle that passes through the points (2,3), (4,5), and (0,-3).
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\n" ); document.write( "Use determinants.
\n" ); document.write( "For this circle:
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document.write( "|(x^2+y^2)   x   y   1|\r\n" );
document.write( "|   13       2   3   1|\r\n" );
document.write( "|   41       4   5   1| = 0\r\n" );
document.write( "|    9       0  -3   1|\r\n" );
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\n" ); document.write( "You can make an Excel sheet to solve it.
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\n" ); document.write( "Or, a geometrical approach:
\n" ); document.write( "Find an equation of the circle that passes through the points A(2,3), B(4,5), and C(0,-3).
\n" ); document.write( "I labeled the points.
\n" ); document.write( "Find the perpendicular bisectors of AB and BC.
\n" ); document.write( "The intersection of the bisectors is the center of the circle, (h,k).
\n" ); document.write( "The distance from the center to any of the 3 points is the radius, r.
\n" ); document.write( " $\"%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2\"$ \r
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