document.write( "Question 723467: I need the step by step process to classify this conic section using the discriminant I was sick the day of the lesson and really have no clue on how to begin I would greatly appreciate it if you could include the equation that this problem is based on also.-
\n" ); document.write( " $\"+6x%5E2-2y%5E2%2B24x%2B2y-1=0+\"$ \n" ); document.write( "

Algebra.Com's Answer #443193 by MathLover1(20850) $\"\"$ $\"About$

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The discriminant of the equation $\"Ax%5E2+%2B+Bxy+%2B+Cy%5E2+%2B+Dx+%2B+Ey+%2B+F+=+0\"$ is the quantity $\"B%5E2+-+4AC\"$ .\r
\n" ); document.write( "\n" ); document.write( "Assuming $\"A\"$ , $\"B\"$ and $\"C\"$ are $\"not\"$ $\"+all\"$ $\"+0\"$ and that degenerate cases are excluded.\r
\n" ); document.write( "\n" ); document.write( "Then,\r
\n" ); document.write( "\n" ); document.write( "if $\"B%5E2+-+4AC+%3C+0\"$ , the graph is an $\"ellipse\"$ or a $\"circle\"$
\n" ); document.write( "if $\"B%5E2+-+4AC+=+0\"$ , the graph is a $\"parabola\"$
\n" ); document.write( "if $\"B%5E2+-+4AC+%3E+0\"$ , the graph is a $\"hyperbola\"$ \r
\n" ); document.write( "\n" ); document.write( " you have \r
\n" ); document.write( "\n" ); document.write( " $\"6x%5E2-2y%5E2%2B24x%2B2y-1=0\"$ .....where $\"A=6\"$ , $\"B=0\"$ , $\"C=-2\"$ , $\"D=24\"$ , $\"E=2\"$ , and $\"F=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"B%5E2+-+4AC=0%5E2+-+4%2A6%2A%28-2%29=-24%2A%28-2%29=48\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"B%5E2+-+4AC+%3E+0\"$ , the graph is a $\"hyperbola\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+6x%5E2-2y%5E2%2B24x%2B2y-1%3E=0%29+\"$ \n" ); document.write( "

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