document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=442912>Question 442912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you show a step by step process of turning x^2+y^2-6x-2y+6 into standard form for a hyperbola? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #305516 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=305516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It may be best to complete the square here:\r<BR>\n" );
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document.write( "Let's make a couple groupings here:\r<BR>\n" );
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document.write( "[x^2-6x] + [y^2 -2y] = -6\r<BR>\n" );
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document.write( "Let's complete the square with the x's.\r<BR>\n" );
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document.write( "Recall, to complete the square, take the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28b%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and make that the c term.\r<BR>\n" );
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document.write( "So our c will be (-6/2)^2 = 9\r<BR>\n" );
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document.write( "[x^2-6x + 9] + [y^2 -2y] = -6 + 9   \r<BR>\n" );
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document.write( "You must balance the equation by adding what you added to the xs.\r<BR>\n" );
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document.write( "Same process with the ys.\r<BR>\n" );
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document.write( "[x^2-6x+9] + [y^2 -2y + 1] = -6 + 9 + 1\r<BR>\n" );
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document.write( "The reason we did this was so we can now factor the xs and ys into a square.\r<BR>\n" );
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document.write( "[x^2-6x + 9] = (x-3)^2  ... it will always be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%28b%2F2%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B%28b%2F2%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "[y^2-2y + 1] = (y-1)^2\r<BR>\n" );
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document.write( "So now we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+%2B+%28y-1%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+%2B+%28y-1%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "To be in standard form, we must be in this form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-h%29%5E2%29%2Fa%5E2+-+%28%28y-k%29%5E2%29%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28%28x-h%29%5E2%29%2Fa%5E2+-+%28%28y-k%29%5E2%29%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We have a problem.\r<BR>\n" );
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document.write( "This is actually the equation for a circle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2+%2B+%28y-1%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2+%2B+%28y-1%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells us we are centered  at (3,1)  with a radius of 2. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Csqrt%284-%28x-3%29%5E2%29+%2B+1%2C+-sqrt%284-%28x-3%29%5E2%29+%2B+1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Is it possible that either the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is supposed to be negative? Then you'd have yourself a hyperbola.<BR>\n" );
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