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find the equation of the circle concentric with the circle x^2+y^2-4x+6y-17=0 which has a tangent of 3x-4y+7=0.
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\n" ); document.write( "Find the center of the circles:
\n" ); document.write( "x^2+y^2-4x+6y-17=0
\n" ); document.write( "x^2+y^2-4x+6y = 17
\n" ); document.write( "(x^2 - 4x + 4) + (y^2 + 6y + 9 = 17 + 4 + 9 = 30
\n" ); document.write( "(x-2)^2 + (y+3)^2 = 30
\n" ); document.write( "Center at (2,-3)
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\n" ); document.write( "Find the distance from the center to the line:
\n" ); document.write( "The slope of the line is 3/4
\n" ); document.write( "The slope of lines perpendicular is -4/3
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\n" ); document.write( "The line thru (2,-3) with a slope of -4/3 ---> y+3 = (-4/3)*(x-2)
\n" ); document.write( "y + 3 = -4x/3 + 8/3
\n" ); document.write( "3y = -4x - 1
\n" ); document.write( "4x + 3y = -1
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\n" ); document.write( "Find the intersection with 3x-4y+7=0
\n" ); document.write( "3x-4y = -7
\n" ); document.write( "4x+3y = -1
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\n" ); document.write( "9x - 12y = -21
\n" ); document.write( "16x +12y = -4
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\n" ); document.write( "25x = -25
\n" ); document.write( "x = -1
\n" ); document.write( "-3 - 4y = -7
\n" ); document.write( "-4y = -4
\n" ); document.write( "y = 1
\n" ); document.write( "---> the intersection is (-1,1)
\n" ); document.write( "Find the distance from the center at (2,-3) to (-1,1)
\n" ); document.write( "d^2 = diffy^2 + diffx^2 = 4^2 + 3 = 25
\n" ); document.write( "---> the circle is (x-2)^2 + (y+3)^2 = 25\r
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