document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=566563>Question 566563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> X^2-10x+37+4y^2+16y=0\r<BR>\n" );
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document.write( "I need the following:\r<BR>\n" );
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document.write( "Center<BR>\n" );
document.write( "foci<BR>\n" );
document.write( "Major axis<BR>\n" );
document.write( "Minor Axis\r<BR>\n" );
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document.write( "I get stuck due to -8 issue\r<BR>\n" );
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document.write( "I a stuck </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #366271 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=366271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Your -8 issue is a self-inflicted wound.  Properly done, -8 never appears anywhere in this problem.  Also, take care how you type your expressions in the future:  X and x are NOT the same thing, so technically you have a three variable equation.  Just sayin'\r<BR>\n" );
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document.write( "First complete the squares:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 10x\ +\ 37\ +\ 4y^2\ +\ 16y\ =\ 0\">\r<BR>\n" );
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document.write( "Constants on the right!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 10x\ +\ \ \ \ +\ 4y^2\ +\ 16y\ =\ -37\">\r<BR>\n" );
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document.write( "Divide the 1st order <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> term coefficient by 2, square the result, add the new constant to both sides:  -10 divided by 2 is -5, -5 squared is 25.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 10x\ +\ 25\ +\ 4y^2\ +\ 16y\ =\ -37\ +\ 25\"> \r<BR>\n" );
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document.write( "Factor a 4 out of both <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 10x\ +\ 25\ +\ 4\left(y^2\ +\ 4y\ \ \ \right)\ =\ -37\ +\ 25\">\r<BR>\n" );
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document.write( "4 divided by 2 is 2. 2 squared is 4.  4 inside the parentheses, 16 outside.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 10x\ +\ 25\ +\ 4\left(y^2\ +\ 4y\ +\ 4 \right)\ =\ -37\ +\ 25\ +\ 16\">\r<BR>\n" );
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document.write( "Factor the two perfect square trinomials and collect terms in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 5)^2\ +\ 4(y\ +\ 2)^2\ =\ 4\">\r<BR>\n" );
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document.write( "Divide through by the RHS constant so that the RHS becomes 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\ -\ 5)^2}{4}\ +\ \frac{(y\ +\ 2)^2}{1}\ =\ 1\">\r<BR>\n" );
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document.write( "Compare to the equation of an ellipse centered at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (h,k)\">, axes parallel to the coordinate axes, major axis measuring <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2a\">, minor axis measuring <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2b\">, and foci at a distance of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{a^2\ -\ b^2}\"> from the center on the major axis.\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( "So your center is at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (5,-2)\">.  Foci at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (5\ +\ \sqrt{3},-2)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (5\ -\ \sqrt{3},-2)\">.  Major axis measures 4.  Minor axis measures 2.\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" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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