document.write( "Question 1191477: Find the equation of the concentric circle to the circle x^2+y^2-4x+6y-17=0 which has a tangent of 3x-4y+7=0. \n" ); document.write( "

Algebra.Com's Answer #823277 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Find the equation of the concentric circle to the circle x^2+y^2-4x+6y-17=0 which has a tangent of 3x-4y+7=0.
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document.write( "By completing the square method, find the center of the circle.  It is the point (2,-3).\r\n" );
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document.write( "To find the radius of the required circle, find the distance from the center (2,-3) to the given line 3x-4y+7=0.\r\n" );
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document.write( "For finding the distance from a given point to a straight line, there is a remarkable formula.\r\n" );
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document.write( "    Let the straight line in a coordinate plane is defined in terms of its linear equation \r\n" );
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document.write( "         a*x + b*y + c = 0,\r\n" );
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document.write( "    where \"a\", \"b\" and \"c\" are real numbers, and let P = (,) be the point in the coordinate plane. \r\n" );
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document.write( "    Then the distance from the point P to the straight line is equal to\r\n" );
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document.write( "        d = .\r\n" );
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document.write( "Regarding this formula, see the lesson\r\n" );
document.write( "    The distance from a point to a straight line in a coordinate plane\r\n" );
document.write( "in this site.\r\n" );
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document.write( "Your straight line is 3x - 4y + 7 = 0.\r\n" );
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document.write( "Substitute the given data  a= 3, b= -4, c= 7,   = 2,  = -3  into the formula to get the distance under the question\r\n" );
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document.write( "     =  =  = 5.\r\n" );
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document.write( "Thus the radius of the circle should be 5 units.\r\n" );
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document.write( "Then the standard form equation of the circle is\r\n" );
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document.write( "     +  = 25.      ANSWER\r\n" );
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