document.write( "Question 534153: determine the equation of the circle whose center is at (4,5) and tangent to the circle whose equation is x^2+y^2+4x+6y-23=0. \n" ); document.write( "
Algebra.Com's Answer #351334 by KMST(5328)\"\" \"About 
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The given circle equation can be written as
\n" ); document.write( "\"+x%5E2%2By%5E2%2B4x%2B6y=23\"
\n" ); document.write( "and completing squares as
\n" ); document.write( "\"+x%5E2%2B4x%2B4%2By%5E2%2B6y%2B9=23%2B4%2B9\" or \"%28x%2B2%29%5E2%2B%28y%2B3%29%5E2=36\"
\n" ); document.write( "showing that its radius is 6 and its center is (-2, -3).
\n" ); document.write( "The distance between the centers is
\n" ); document.write( "
\n" ); document.write( "If the circles meet in between the centers (they are externally tangent), the radius of the second circle will be
\n" ); document.write( "\"10-6=4\"
\n" ); document.write( "and the equation for the second circle will be
\n" ); document.write( "\"%28x-4%29%5E2%2B%28y-5%29%5E2=16\"
\n" ); document.write( "which can be written as
\n" ); document.write( "\"+x%5E2%2By%5E2-8x-10y%2B25=0\"
\n" ); document.write( "If we make the second circle contain the first one (internally tangent circles), then the radius would be
\n" ); document.write( "\"10%2B6=16\"
\n" ); document.write( "and the equation for the second circle would be
\n" ); document.write( "\"%28x-4%29%5E2%2B%28y-5%29%5E2=256\"
\n" ); document.write( "which can be written as
\n" ); document.write( "\"+x%5E2%2By%5E2-8x-10y-215=0\"
\n" ); document.write( "
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