document.write( "Question 278068: i'm learning about ellipses and i have the problem:
\n" ); document.write( "x squared+4y squared-6x+24y+41=0
\n" ); document.write( "i need to find the center, foci, and vertices.
\n" ); document.write( "i have no idea how to even start, i tried by first completing the square but i'm missing something because i get confused by that 41 that is thrown in there, please help. \n" ); document.write( "

Algebra.Com's Answer #202462 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
i'm learning about ellipses and i have the problem:
\n" ); document.write( "x squared+4y squared-6x+24y+41=0
\n" ); document.write( "i need to find the center, foci, and vertices.
\n" ); document.write( "i have no idea how to even start, i tried by first completing the square but i'm missing something because i get confused by that 41 that is thrown in there, please help.
\n" ); document.write( "

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document.write( "Get the number on the right by adding  to both sides:\r\n" );
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document.write( "Swap the two middle terms to get the -term next to the -term\r\n" );
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document.write( "Multiply the coefficient of x, which is , by ,\r\n" );
document.write( "get  then square that number  which \r\n" );
document.write( "gives \r\n" );
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document.write( "Now add  to both sides:\r\n" );
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document.write( "Since the  term has a coefficient other than 1,\r\n" );
document.write( "factor the 4 out of the last two terms on the left:\r\n" );
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document.write( "Now we complete the square inside the parentheses.\r\n" );
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document.write( "Multiply the coefficient of y, which is , by ,\r\n" );
document.write( "get  then square that number  which \r\n" );
document.write( "gives \r\n" );
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document.write( "Now we add  inside the parentheses.  However\r\n" );
document.write( "when we add  inside the parentheses we are REALLY\r\n" );
document.write( "adding  or  to the left side \r\n" );
document.write( "because everything in the parentheses is multiplied by the \r\n" );
document.write( "in front of the parentheses.  So we add  to the right side:\r\n" );
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document.write( "Now we factor the first three terms as  or \r\n" );
document.write( "and we factor the three terms inside the parentheses as \r\n" );
document.write( "or , and combine the numbers on the right as \r\n" );
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document.write( "Now to get 1 on the right we divive every term through by 4\r\n" );
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document.write( "Notice that I left a 1 under the bottom of the second term\r\n" );
document.write( "so that it would be in standard form\r\n" );
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document.write( "Since  is larger than  and the larger term is under\r\n" );
document.write( "the  term it is in the form\r\n" );
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document.write( "and has its major axis horizontal.\r\n" );
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document.write( ", , , so \r\n" );
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document.write( ", so , so we plot the center {3,-3)\r\n" );
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document.write( "Then we draw the major axis by drawing a horizontal line \r\n" );
document.write( "units both right and left of the center (3,-3)\r\n" );
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document.write( "Now we can get the vertices, for they are the points ar the ends\r\n" );
document.write( "of the major axis, and we can see that the major axis, the green\r\n" );
document.write( "line segment starts at (1,-3) on the left and goes to (5,-3) on\r\n" );
document.write( "the right, so the vertices are\r\n" );
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document.write( "(1,-3) and (5,-3)\r\n" );
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document.write( "Now we draw the minor axis by drawing a horizontal line \r\n" );
document.write( "units both up and down from the center (3,-3):\r\n" );
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document.write( "Now we can sketch in the ellipse:\r\n" );
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document.write( "Finally we need to find the foci.  The distance from\r\n" );
document.write( "the center to each focus is  and  is\r\n" );
document.write( "calculated by this Pythagorean identity:\r\n" );
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document.write( "The coordinates of the foci are\r\n" );
document.write( "points which are distance of \r\n" );
document.write( "units right and left of the center on the major axis,\r\n" );
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document.write( "so the two foci are these points: \r\n" );
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document.write( "(3-�3,-3) and (3+�3,-3)\r\n" );
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document.write( "They are plotted below:\r\n" );
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document.write( "Edwin

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