document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189360>Question 189360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the standard form of the ellipse given by the equation   x^2 + 25y^2 -2x + 150y + 201 = 0  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142069 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The only difference (aside from the values of the coefficients) between the equation of the hyperbola that I just showed you earlier and an ellipse is that a hyperbola has a minus sign between the two fractions on the left and an ellipse has a plus sign.  The process of completing the squares is the same.\r<BR>\n" );
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document.write( "An ellipse centered at (<i>h</i>,<i>k</i>) with a semi-major axis <i>a</i>, and a semi-minor axis <i>b</i> is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{(x - h)^2}{a^2} + \frac{ (y - k)^2}{b^2} = 1\">\r<BR>\n" );
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document.write( "Notice that if <i>a</i> = <i>b</i> and then you multiply by the now common denominator, you get the equation of a circle centered at (<i>h</i>,<i>k</i>) with radius <i>a</i>.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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