document.write( "Question 968527: Good Morning, Can anyone show me the steps for this, please?
\n" ); document.write( "Consider the following equation and determine if it is a parabola, an ellipse, or a hyperbola and sketch it's graph:
\n" ); document.write( "4y^2+6x−2y+3x^2−15=2y^2+4x^2
\n" ); document.write( "Thank you in advance for your help. \n" ); document.write( "

Algebra.Com's Answer #591825 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4y%5E2%2B6x-2y%2B3x%5E2-15=2y%5E2%2B4x%5E2\"$
\n" ); document.write( "Does this solution process contain a mistake?
\n" ); document.write( " $\"3x%5E2%2B6x%2B4y%5E2-2y-15-2y%5E2-4x%5E2=0\"$
\n" ); document.write( " $\"-x%5E2%2B6x%2B2y%5E2-2y-15=0\"$
\n" ); document.write( " $\"x%5E2-6x-2y%5E2%2B2y%2B15=0\"$
\n" ); document.write( "Complete The Squares for x and y
\n" ); document.write( " $\"x%5E2-6x%2B9-2%28y%5E2-y%29%2B15=9\"$
\n" ); document.write( " $\"%28x-3%29%5E2-2%28y%5E2-y%2B1%2F4%29%2B15=9%2B%28-1%2F2%29\"$
\n" ); document.write( " $\"%28x-3%29%5E2-2%28y-1%2F2%29%5E2%2B15=8%261%2F2\"$
\n" ); document.write( " $\"%28x-3%29%5E2-2%28y-1%2F2%29%5E2=8.5-15=-6.5\"$
\n" ); document.write( " $\"-%28x-3%29%5E2%2B2%28y-1%2F2%29%5E2=6.5\"$
\n" ); document.write( " $\"-%28x-3%29%5E2%2F6.5%2B%28y-1%2F2%29%5E2%2F%286.5%2F2%29=1\"$
\n" ); document.write( "Possible mistake but at least steps still lead to hyperbola with vertex on the y axis but not on the x-axis.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Sign mistake, MAYBE made.
\n" ); document.write( "A way to avoid that, if it actually happened, could be to start with all x on one side and all y on the other side, and then perform Completion of the Squares.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"4y%5E2%2B6x-2y%2B3x%5E2-15=2y%5E2%2B4x%5E2\"$
\n" ); document.write( " $\"4y%5E2-2y-15=-6x-3x%5E2%2B4x%5E2\"$
\n" ); document.write( " $\"4y%5E2-2y-15=x%5E2-6x\"$
\n" ); document.write( " $\"4%28y%5E2-%281%2F2%29y%29-15=x%5E2-6\"$
\n" ); document.write( " $\"4%28y%5E2-%281%2F2%29y%2B1%2F4%29-15-4%281%2F4%29=%28x%5E2-6x%2B9-9%29\"$
\n" ); document.write( " $\"4%28y-1%2F2%29%5E2-15-1=%28x-3%29%5E2-9\"$
\n" ); document.write( " $\"4%28y-1%2F2%29%5E2-16=%28x-3%29%5E2-9\"$
\n" ); document.write( " $\"4%28y-1%2F2%29%5E2-%28x-3%29%5E2=-9%2B16\"$
\n" ); document.write( " $\"4%28y-1%2F2%29%5E2-%28x-3%29%5E2=7\"$
\n" ); document.write( " $\"%284%2F7%29%28y-1%2F2%29%5E2-%28x-7%29%5E2%2F7=1\"$
\n" ); document.write( " $\"%28y-1%2F2%29%5E2%2F%287%2F4%29-%28x-7%29%5E2%2F7=1\"$ -----Without checking through a solution a third time, this one is probably correct for less likely to have made arithmetic mistakes.
\n" ); document.write( "Still hyperbola with vertices on the y axis IF were in a form centered at the origin; but this one is centered at ( 7, 1/2 ). \n" ); document.write( "

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