document.write( "Question 510: this is an Ellipses problem but I can't figure it out. Could you please help me. \r
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Algebra.Com's Answer #175 by AnlytcPhil(1806) $\"\"$ $\"About$

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>>...this is an Ellipses problem but I can't figure it out. \r\n" );
document.write( "Could you please help me. x^2+4y^2-10x-40y+121=0...<<\r\n" );
document.write( "          x² + 4y² - 10x - 40y + 121 = 0\r\n" );
document.write( "Group x terms together and y-terms together and get the 121 off the left side:\r\n" );
document.write( "                x² - 10x + 4y² - 40y = -121 \r\n" );
document.write( "Factor the coefficients of x and y out of the pairs of terms in each \r\n" );
document.write( "variable:\r\n" );
document.write( "           1(x² - 10x) + 4(y² - 10y) = -121\r\n" );
document.write( "Complete the square in each of the parentheses.  Take half the \r\n" );
document.write( "coefficients of x or y, respectively, and square them.  We need to \r\n" );
document.write( "add 25 in the first parentheses and 25 in the second.  To offset this \r\n" );
document.write( "we must add 1∙25 and 4∙25 to the right side:\r\n" );
document.write( " 1(x² - 10x + 25) + 4(y² - 10y + 25) = -121 + 1∙25 + 4∙25  \r\n" );
document.write( "Factor the trinomials in the parentheses as perfect squares:\r\n" );
document.write( "               1(x - 5)² + 4(y - 5)² = -121 + 25 + 100\r\n" );
document.write( "                (x - 5)² + 4(y - 5)² = 4\r\n" );
document.write( "Divide every term through by 4 to get 1 on the right\r\n" );
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document.write( "a² > b², so this is of the form \r\n" );
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document.write( "an ellipse with horizontal major axis,\r\n" );
document.write( "which has center at (h,k) = (5,5), a²=4, so a=2 = semi-major axis,\r\n" );
document.write( "b²=1, so b=1 = semi-minor axis.   \r\n" );
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document.write( "Edwin

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