document.write( "Question 1168435: If the circle is tangent to the line -3x+2y+1=0 at the point (1, 1), and the center is an the line x+y-1=0. Find the general equation of the circle. \n" ); document.write( "
Algebra.Com's Answer #793323 by Edwin McCravy(20055)\"\" \"About 
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If the circle is tangent to the line -3x+2y+1=0 at the point (1, 1), and the
\n" ); document.write( "center is an the line x+y-1=0. Find the general equation of the circle.
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document.write( "Let the equation of the circle be:\r\n" );
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document.write( "\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"\r\n" );
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document.write( "Then the tangent point (1,1) is on the circle, so\r\n" );
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document.write( "\"%281-h%29%5E2%2B%281-k%29%5E2=r%5E2\"\r\n" );
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document.write( "The center (h,k) lies on the line \r\n" );
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document.write( "\"x%2By-1=0\", so\r\n" );
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document.write( "\"h%2Bk-1=0\"\r\n" );
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document.write( "The perpendicular distance from the center (h,k), to the tangent line, \r\n" );
document.write( "which is\r\n" );
document.write( "\"-3x%2B2y%2B1=0\"\r\n" );
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document.write( "is the radius r (in green), so\r\n" );
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document.write( "\"%28-3h%2B2k%2B1%29%2Fsqrt%2813%29=%22%22+%2B-+r\"\r\n" );
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document.write( "So we have the system of three equations in three unknowns:\r\n" );
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document.write( "Can you find the solution?\r\n" );
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document.write( "The solution is (h,k,r) = (-2,3,√13)\r\n" );
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document.write( "So the equation of the circle is\r\n" );
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document.write( "(x+2)2 + (y-3)2 = 13 \r\n" );
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document.write( "If you have trouble finding the solution to the system,\r\n" );
document.write( "tell me about it in the thank you message below, and I'll\r\n" );
document.write( "get back to you by email.  No charge.\r\n" );
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document.write( "Edwin
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