document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197706>Question 197706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My problem is I have the equation: x^2 - y^2 + 24y > (or equal to) 148<BR>\n" );
document.write( "Well I put it in graphing form which I believe is (x^2)/292 - (y^2+12)/292=1<BR>\n" );
document.write( "Which makes it a Hyperbola, and I need to graph it but the radius is the square root of 292, which is 17.08800749, and that is too big to be graphed on my paper and that can't happen because it has to fit. So what did I do wrong? Could you tell me the correct equation and the vertical and horizontal radius?\r<BR>\n" );
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document.write( "I did not receive this question from a textbook. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148248 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=148248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming you want to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+y%5E2+%2B+24y=148 ALIGN=MIDDLE  ALT=\"x%5E2+-+y%5E2+%2B+24y=148\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+y%5E2+%2B+24y=148 ALIGN=MIDDLE  ALT=\"x%5E2+-+y%5E2+%2B+24y=148\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28y%5E2+-+24y%29=148 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28y%5E2+-+24y%29=148\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the negative from 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;\" > coefficient\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28y%5E2+-+24y%2B144-144%29=148 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28y%5E2+-+24y%2B144-144%29=148\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take half of -24 to get -12. Square it to get 144. Now add AND subtract this value inside the parenthesis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28%28y-12%29%5E2-144%29=148 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28%28y-12%29%5E2-144%29=148\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28y-12%29%5E2%2B144=148 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28y-12%29%5E2%2B144=148\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28y-12%29%5E2=148-144 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28y-12%29%5E2=148-144\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 144 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+%28y-12%29%5E2=4 ALIGN=MIDDLE  ALT=\"x%5E2+-+%28y-12%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2F4+-+%28%28y-12%29%5E2%29%2F4+=+1 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F4+-+%28%28y-12%29%5E2%29%2F4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2F2%5E2+-+%28%28y-12%29%5E2%29%2F2%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F2%5E2+-+%28%28y-12%29%5E2%29%2F2%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 4 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2 ALIGN=MIDDLE  ALT=\"2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-0%29%5E2%29%2F2%5E2+-+%28%28y-12%29%5E2%29%2F2%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28%28x-0%29%5E2%29%2F2%5E2+-+%28%28y-12%29%5E2%29%2F2%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite \"x\" as \"x-0\"\r<BR>\n" );
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document.write( "Now the equation is of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is a hyperbola) where h=0, k=12, a=2, and b=2\r<BR>\n" );
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