document.write( "Question 1186873: What is the equation of the circle with center at (0, 2) and tangent to the line 3x - 4y = 12 \n" ); document.write( "

Algebra.Com's Answer #817851 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "What is the equation of the circle with center at (0, 2) and tangent to the line 3x - 4y = 12
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document.write( "All you need is to find the radius of the circle, i.e. the distance from the point (0,2) \r\n" );
document.write( "to the given straight line  3x - 4y - 12 = 0.\r\n" );
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document.write( "There is a remarkable formula which ideally suits for this need.\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( "Substitute the given data  a= 3, b= -4, c= -12,   = 0,  = 2  into the formula to get the distance under the question\r\n" );
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document.write( "     =  =  = 4.\r\n" );
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document.write( "Answer.  The radius of the circle is 4 units.\r\n" );
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document.write( "         The standard equation of the circle is   +  = .\r\n" );
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