document.write( "Question 1133939: Find the range of values of k, such that the straight line $\"y=3x%2Bk\"$ does not intersect the curve $\"x%5E2%2By%5E2-8=0\"$ . \n" ); document.write( "

Algebra.Com's Answer #752386 by JaydenX(2) $\"\"$ $\"About$

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Substitute $\"y=3x%2Bk\"$ into $\"x%5E2%2By%5E2-8=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B%283x%2Bk%29%5E2-8=0\"$
\n" ); document.write( " $\"x%5E2%2B9x%5E2%2B6kx%2Bk%5E2-8=0\"$
\n" ); document.write( " $\"10x%5E2%2B6kx-8=0\"$ \r
\n" ); document.write( "\n" ); document.write( "Using the formula $\"b%5E2-4ac%3C0\"$ as it doesn’t intersect the curve.
\n" ); document.write( " $\"%286k%29%5E2-4%2810%29%28k%5E2-8%29%3C0\"$
\n" ); document.write( " $\"36k%5E2-40k%5E2%2B320%3C0\"$
\n" ); document.write( " $\"-4k%5E2%2B320%3C0\"$
\n" ); document.write( " $\"4k%5E2%3E320\"$ \r
\n" ); document.write( "\n" ); document.write( "Separate into possible cases,
\n" ); document.write( " $\"k%3Esqrt%2880%29\"$ and $\"-k%3Esqrt%2880%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Hence, the range of values of k,
\n" ); document.write( " $\"k%3Esqrt%2880%29\"$ , $\"k%3C-sqrt%2880%29\"$ \n" ); document.write( "

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