document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=991825>Question 991825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this! Find the centre, vertices, lenght of latus rectum, foci , eccentricities of the ellipse x^2 + 9y^2 + 4x -18y - 23 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611573 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=611573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "x^2 + 9y^2 + 4x -18y - 23 = 0<BR>\n" );
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document.write( "Complete the squares:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+9y%5E2+%2B+4x+-18y+-+23 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+9y%5E2+%2B+4x+-18y+-+23\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2+-+4+%2B+%283y-3%29%5E2+-+9+-+23 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2+-+4+%2B+%283y-3%29%5E2+-+9+-+23\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2+%2B+3%5E2%2A%28y-1%29%5E2+-+36 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2+%2B+3%5E2%2A%28y-1%29%5E2+-+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So, &nbsp;you have the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A%28y-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"9%2A%28y-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "or, &nbsp;in the canonical form,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%2F6%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2F6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-1%29%5E2%29%2F%282%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28y-1%29%5E2%29%2F%282%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "It is a canonical equation of an ellipse. \r<BR>\n" );
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document.write( "Its center is at the point &nbsp;(x,y) = (-2,1). &nbsp;Semi-major and semi-minor axes are &nbsp;6&nbsp; and &nbsp;2, &nbsp;respectively: &nbsp;a=6 &nbsp;and &nbsp;b=2. \r<BR>\n" );
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document.write( "Semi-major axis is the distance from the ellipse' center to its vertices. \r<BR>\n" );
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document.write( "Linear eccentricity is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286%5E2+-+2%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%286%5E2+-+2%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2832%29 ALIGN=MIDDLE  ALT=\"sqrt%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. &nbsp;It is the distance from the ellipse's center to its foci. \r<BR>\n" );
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document.write( "Next, &nbsp;take the textbook and determine the rest ellipse's characteristics you need.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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