document.write( "Question 315531: please help me solve this question:
\n" ); document.write( "y^2+2y=x^2+x
\n" ); document.write( " is this equation a parabola, circle, ellipse, or hyperbola? how do you know?
\n" ); document.write( "thnks \n" ); document.write( "
Algebra.Com's Answer #225745 by Edwin McCravy(20059)\"\" \"About 
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please help me solve this question:
\n" ); document.write( "y2 + 2y = x2 + x
\n" ); document.write( " is this equation a parabola, circle, ellipse, or hyperbola? how do you know?
\n" ); document.write( "thnks
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document.write( "Get it in the standard conic form:\r\n" );
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document.write( "Ax2 + Bxy + Cy2 + Dx + Ey + F = 0\r\n" );
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document.write( "then calculate the discriminant, which is B2 - 4AC\r\n" );
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document.write( "1. If the discriminant is positive, the equation represents a hyperbola.\r\n" );
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document.write( "2. If the discriminant is zero, the equation represents a parabola.\r\n" );
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document.write( "3. If the discriminant is negative then it is either an ellipse or a circle.\r\n" );
document.write( "   If it's a circle, then B=0 and A=C, otherwise it's an ellipse.\r\n" );
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document.write( "So let's get\r\n" );
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document.write( "y2 + 2y = x2 + x\r\n" );
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document.write( "in the standard conic form \r\n" );
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document.write( "Ax2 + Bxy + Cy2 + Dx + Ey + F = 0\r\n" );
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document.write( "Get 0 on the right by subtracting the right side from both sides:\r\n" );
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document.write( "y2 + 2y - x2 - x = 0\r\n" );
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document.write( "Now lets rearrange the terms in the order as they appear in the standard\r\n" );
document.write( "conic form:\r\n" );
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document.write( " Ax2 + Bxy + Cy2 + Dx + Ey + F = 0\r\n" );
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document.write( "-1x2 + 0xy + 1y2 - 1x + 2y + 0 = 0\r\n" );
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document.write( "So A=-1, B=0, C=1, D=-1, E=2, F=0\r\n" );
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document.write( "B2 - 4AC = (0)^2 - 4(-1)(1) = 0 - (-4) = 0 + 4 = 4\r\n" );
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document.write( "That's positive, so the equation represents a hyperbola.\r\n" );
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document.write( "-----------------------------------\r\n" );
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document.write( "Edwin
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