document.write( "Question 1183327: A circle is tangent to the line 3x-4y -4 = 0 at the point (-4,-4) and the center is on the line
\n" ); document.write( "x+y+7 = 0. Find the equation of the circle
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Algebra.Com's Answer #813579 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "Any straight line, perpendicular to the line 3x - 4y - 4 = 0, has an equation\r\n" );
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document.write( "    4x + 3y = c,\r\n" );
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document.write( "where c is some constant.  The perpendicular line, passing through the point (-4,-4), has the constant \"c\" equal to \r\n" );
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document.write( "    4*(-4) + 3*(-4) = -16 + -12 = -28.\r\n" );
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document.write( "So, the circle center is the intersection of the lines\r\n" );
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document.write( "    4x + 3y = -28     (1)\r\n" );
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document.write( "     x +  y =  -7     (2)\r\n" );
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document.write( "It is easy to solve (Elimination or Substitution, on your choice).\r\n" );
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document.write( "The intersection point is  y = 0, x = -7.\r\n" );
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document.write( "Thus the center of the circle is the point (x,y) = (-7,0).\r\n" );
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document.write( "The radius of the circle is the distance from its center (-7,0) to the point (-4,-4)\r\n" );
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document.write( "    r =  =  = 5.\r\n" );
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document.write( "Thus the center of the circle is the point (-7,0)  and its radius is 5 units.\r\n" );
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document.write( "The standard equation of the circle is\r\n" );
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document.write( "     +  = 25.    ANSWER\r\n" );
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