document.write( "Question 1083792: For what value of k the line 2x-y+k=0 is tangent to the parabola y^2=6x? \n" ); document.write( "

Algebra.Com's Answer #697845 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "For what value of k the line 2x-y+k=0 is tangent to the parabola y^2=6x?
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document.write( "The key idea of solving this problem is that the system\r\n" );
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document.write( "2x - y + k = 0,     (1)\r\n" );
document.write( " = 6x      (2)\r\n" );
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document.write( "must have one and only one solution.\r\n" );
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document.write( "    (Then the solution will be the tangent point).\r\n" );
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document.write( "From equation (1), express 2x = y - k and substitute it into equation (2):\r\n" );
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document.write( " = 3*(2x),   or\r\n" );
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document.write( " = 3*(y-k),\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "The discriminant of this quadratic equation is \r\n" );
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document.write( "d =  = 9 - 12k.\r\n" );
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document.write( "The condition of having the unique solution is d = 0,   or\r\n" );
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document.write( "9 - 12k = 0,\r\n" );
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document.write( "which gives you k =  = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. k = $\"3%2F4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Parabola $\"y%5E2\"$ = 6x and the straight line 2x - y + $\"3%2F4\"$ = 0.\r
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\n" ); document.write( "\n" ); document.write( "Ignore writing by \"josgarithmetic\" since his conception and explanation are WRONG.\r
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