document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=391114>Question 391114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What would these equations be in standard form??? <BR>\n" );
document.write( "I know that this is a hyperbola - x^2-y^2-8x+10y+15=0<BR>\n" );
document.write( "And this is a parabola - y^2+4y-8x+4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #277412 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=277412\">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( "Complete the square:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ y^2\ -\ 8x\ +\ 10y\ +\ 15\ =\ 0\">\r<BR>\n" );
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document.write( "Constant to the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ y^2\ -\ 8x\ +\ 10y\ =\ -15\">\r<BR>\n" );
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document.write( "Group similar terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ -\ y^2\ +\ 10y\ =\ -15\">\r<BR>\n" );
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document.write( "Divide the x-terms by the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2\">.  Since this is already 1, skip this step.\r<BR>\n" );
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document.write( "Divide the coefficent on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> term by 2, square the result, then add that result to both sides of the equation.  -8 divided by 2 is -4.  -4 squared is 16.  Add 16 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ +\ 16\ -\ y^2\ +\ 10y\ =\ -15\ +\ 16\">\r<BR>\n" );
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document.write( "Divide the y-terms by the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y^2\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ +\ 16\ -\ \left(y^2\ -\ 10y\right)\ =\ -15\ +\ 16\">\r<BR>\n" );
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document.write( "Divide the coefficent on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> term by 2, square the result, then add that result to both sides of the equation.  -10 divided by 2 is 5.  5 squared is 25.  But consider the -1 coefficient in front of the parentheses.  Add -25 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 8x\ +\ 16\ -\ \left(y^2\ -\ 10y\ + 25\right)\ =\ -15\ +\ 16\ -\ 25\">\r<BR>\n" );
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document.write( "Factor the two perfect square trinomials in the LHS 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\ -\ 4)^2\ -\ (y\ -\ 5)^2\ =\ -24\">\r<BR>\n" );
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document.write( "Divide both sides by -24:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(y\ -\ 5)^2}{24}\ -\ \frac{(x\ -\ 4)^2}{24}\ =\ 1\">\r<BR>\n" );
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document.write( "One problem per post, please.\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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