document.write( "Question 863824: The centre of a circle lies on the x-axis and passes through the points (4,5) and (-2,3). Find the equation of the circle in the form x^2+y^2+2gx+2fy+c=0 \n" ); document.write( "

Algebra.Com's Answer #520639 by stanbon(75887) $\"\"$ $\"About$

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The centre of a circle lies on the x-axis and passes through the points (4,5) and (-2,3). Find the equation of the circle in the form x^2+y^2+2gx+2fy+c=0
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\n" ); document.write( "Plot the points; let the center be (x,0)
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\n" ); document.write( "Radii are equal::
\n" ); document.write( "sqrt[(4-x)^2 + (5-0)^2] = sqrt[(-2-x)^2+(3-0)^2]
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\n" ); document.write( "(4-x)^2 + 5^2 = (2+x)^2+9
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\n" ); document.write( "16-8x+x^2 + 25 = 4 + 4x + x^2 + 9
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\n" ); document.write( "41 - 6x = 13+4x
\n" ); document.write( "10x = 28
\n" ); document.write( "x = 2.8
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\n" ); document.write( "Center is (2.8,0)
\n" ); document.write( "radius = sqrt[(4-2.8)^2 + 25] = sqrt[1.44+ 25] = sqrt(26.44)
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\n" ); document.write( "Equation:
\n" ); document.write( "(x-2.8)^2 + y^2 = 26.44
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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