document.write( "Question 1089590: Pleas help me find the exact values of m for which the line y=mx+5 is a tangent to the curve x^2+y^2=10.\r
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Algebra.Com's Answer #703928 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Substitute y = mx+5 into the circle equation. You will get\r\n" );
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document.write( " = 10,\r\n" );
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document.write( " = 10,\r\n" );
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document.write( " = 0.             (1)\r\n" );
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document.write( "The condition that the straight line is tangent to the circle is equivalent to the fact that the equation (1) has only one root,\r\n" );
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document.write( "which, in turn, means that the discriminant of the equation (1) is equal to zero.\r\n" );
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document.write( "It gives you an equation for m:\r\n" );
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document.write( "d =  = 0.\r\n" );
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document.write( "Simplify and solve it for m:\r\n" );
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document.write( " = 0,\r\n" );
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document.write( " = 40  ====>   =  =   ====>  m = +/- .\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from this solution:\r
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document.write( "    The fact that a line is tangent to the circle is equivalent to the fact that they have only one common point.\r\n" );
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