document.write( "Question 1186874: Find the equation of the circle with center on the point of intersection of the lines x + y - 4 = 0 and 5x + 2y + 1 = 0, with radius of 5 units. \n" ); document.write( "

Algebra.Com's Answer #817852 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Find the equation of the circle with center on the point of intersection of the lines x + y - 4 = 0 and 5x + 2y + 1 = 0,
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document.write( "All you need is to find the coordinates of the center of the circle, i.e. the intersection point of the given lines.\r\n" );
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document.write( "For it, you need to solve the system of linear equations\r\n" );
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document.write( "     x +  y =  4,    (1)\r\n" );
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document.write( "    5x + 2y = -1.    (2)\r\n" );
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document.write( "From equation (1), express y = 4-x  and substitute it into equation (2).  You will get single equation for x\r\n" );
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document.write( "    5x + 2*(4-x) = -1,\r\n" );
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document.write( "    5x + 8 - 2x = -1\r\n" );
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document.write( "       3x       = -1 - 8\r\n" );
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document.write( "       3x       = -9\r\n" );
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document.write( "        x       = -9/3 = -3.\r\n" );
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document.write( "Now from equation (1)  y = 4 - x = 4 - (-3) = 4 + 3 = 7.\r\n" );
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document.write( "The center point is  (-3,7);  the standard form circle equation is\r\n" );
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document.write( "     +  = ,\r\n" );
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document.write( "or\r\n" );
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document.write( "     +  = 25.    ANSWER\r\n" );
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