document.write( "Question 1056901: For what value/s of k will the system of equations x^2 + y^2 = 4 and y=kx+4 have exactly two points? \n" ); document.write( "

Algebra.Com's Answer #671965 by ikleyn(52797) $\"\"$ $\"About$

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For what value/s of k will the system of equations x^2 + y^2 = 4 and y=kx+4 have exactly two points?
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document.write( " = 4,      (1)\r\n" );
document.write( "y = kx + 4.       (2)\r\n" );
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document.write( "Substitute the expression y = kx + 4 from (2) into equation (1). You will get\r\n" );
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document.write( " = 4.\r\n" );
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document.write( "Simplify\r\n" );
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document.write( " = 4,\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "In order for the last equation has two different real roots, the discriminant must be positive:\r\n" );
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document.write( "d = b^2 - 4ac = (8k)^2 - 4*(1+k^2)*12 > 0,  or\r\n" );
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document.write( "    64k^2 - 48k^2 - 48 > 0,   or\r\n" );
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document.write( "    16k^2 > 48,   or\r\n" );
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document.write( "    k^2 > 3,   or\r\n" );
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document.write( "    k <   OR  k > .\r\n" );
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document.write( "Answer. The solution set is (,) U (,).\r\n" );
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