document.write( "Question 1143792: find the equation of the circle woth center at (-3,8) and tangent to the line
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Algebra.Com's Answer #764695 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "As soon as you find the radius of the circle, you will be in position to write its equation.\r\n" );
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document.write( "The radius of the circle is equal to the distance from the given center to the given line.\r\n" );
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document.write( "To find this distance, use the general formula for the distance from the point (p,q) to the line Ax + By + C = 0\r\n" );
document.write( "in the coordinate plane\r\n" );
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document.write( "    d = .      (1)\r\n" );
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document.write( "In your case  A= 1, B= -1, C= 5, p= -3, q= 8.\r\n" );
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document.write( "So from the formula (1), the distance from the point (-3,8) to the line x-y+5 = 0 is\r\n" );
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document.write( "    d =  = .\r\n" );
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document.write( "Thus the radius of the circle is  r = d = .\r\n" );
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document.write( "Then the standard equation of the circle is\r\n" );
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document.write( "     +  = ,\r\n" );
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document.write( "or, equivalently,\r\n" );
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document.write( "     +  = 18.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Regarding the basic formula (1), see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - The distance from a point to a straight line in a coordinate plane \r
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\n" ); document.write( "\n" ); document.write( "    - Using formula for the distance from a point to a straight line in a plane to solve word problems \r
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