document.write( "Question 1013853: Find the equation of the circle if the circle is tangent to the line 3x+y+2=0 at (-1,1) and it passes through the point (3,5). \n" ); document.write( "
Algebra.Com's Answer #630147 by Alan3354(69443)\"\" \"About 
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Find the equation of the circle if the circle is tangent to the line 3x+y+2=0 at A(-1,1) and it passes through the point B(3,5).
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\n" ); document.write( "The center of the circle will be on the line perpendicular to the given line thru (-1,1).
\n" ); document.write( "y-1 = (1/3)*(x+1) is the line.
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\n" ); document.write( "The center is equidistant from A & B so it's on the perpendicular bisector (PB) of line AB.
\n" ); document.write( "The midpoint of AB is (1,3).
\n" ); document.write( "The slope of AB is 1.
\n" ); document.write( "--> PB is y-3 = -1*(x-1)
\n" ); document.write( "Or y = -x + 4
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\n" ); document.write( "The center is the intersection of y = -x + 4 and y-1 = (1/3)*(x+1)
\n" ); document.write( "-x + 4 = x/3 + 4/3
\n" ); document.write( "-3x + 12 = x + 4
\n" ); document.write( "x = 2
\n" ); document.write( "y = 2
\n" ); document.write( "--> the center is (2,2)
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\n" ); document.write( "The radius is the distance to A or B:
\n" ); document.write( "\"r%5E2+=+3%5E2+%2B+1%5E1+=+10\"
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\n" ); document.write( "\"%28x-2%29%5E2+%2B+%28y-2%29%5E2+=+10\" is the circle.
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