document.write( "Question 635404: Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola .
\n" ); document.write( "x2 + 4y2 + 2x - 24y + 33 = 0 \n" ); document.write( "

Algebra.Com's Answer #400299 by AnlytcPhil(1806) $\"\"$ $\"About$

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document.write( "x² + 4y² + 2x - 24y + 33 = 0\r\n" );
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document.write( "Rearrange equation like this\r\n" );
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document.write( "(x² + 2x) + (4y² - 24y) = -33\r\n" );
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document.write( "(x² + 2x) + 4(y² - 6y) = -33\r\n" );
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document.write( "Complete the square:\r\n" );
document.write( "Multiply the coefficient of each 1st degree term\r\n" );
document.write( " by one-half theb square the result. Then add this\r\n" );
document.write( "inside each set of parentheses, and add the \r\n" );
document.write( "corresponding amount to the right side:\r\n" );
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document.write( "(x² + 2x + 1) + 4(y² - 6y + 9) = -33 + 1 + 36\r\n" );
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document.write( "Note that since 9 was added in the second set of parenthese,\r\n" );
document.write( "that ammounted to adding 36 to both side because of 4 coefficient\r\n" );
document.write( "of the second set of parentheses.\r\n" );
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document.write( "Factor the quadratics inside the parentheses as perfect squarse,\r\n" );
document.write( "and combine terms on the right side:\r\n" );
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document.write( "(x+1)² + 4(y-3)² = 4\r\n" );
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document.write( "Get 1 on the right side by dividing every term though by 4\r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( "Edwin

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