document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=913718>Question 913718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a set of several of these:<BR>\n" );
document.write( "Sketch these curves. (Are they all hyperbolas? Explain.)\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+=+10 ALIGN=MIDDLE  ALT=\"x%5E2+-+y%5E2+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "How do I sketch these, and what makes a hyperbola a hyperbola?<BR>\n" );
document.write( "I hate my textbook. It barely tells you how to do any of these. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554672 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=554672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are many resources on the Internet, you're not stuck with only your textbook any more.<BR>\n" );
document.write( "Hyperbolas have the general form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Fa%29%5E2-%28y%2Fb%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x%2Fa%29%5E2-%28y%2Fb%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You sketch like you would for any function.<BR>\n" );
document.write( "Pick an x, generate a y, plot the ordered pair. <BR>\n" );
document.write( "With both variables being squared, you can save time using symmetry.<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=10 ALIGN=MIDDLE  ALT=\"x%5E2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0+%2B-+sqrt%2810%29 ALIGN=MIDDLE  ALT=\"x=0+%2B-+sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >},<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2Ccircle%28sqrt%2810%29%2C0%2C0.3%29%2Ccircle%28-sqrt%2810%29%2C0%2C0.3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2 ALIGN=MIDDLE  ALT=\"y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2 ALIGN=MIDDLE  ALT=\"y=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4=10 ALIGN=MIDDLE  ALT=\"x%5E2-4=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=14 ALIGN=MIDDLE  ALT=\"x%5E2=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0+%2B-+sqrt%2814%29 ALIGN=MIDDLE  ALT=\"x=0+%2B-+sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814%29 ALIGN=MIDDLE  ALT=\"sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814%29 ALIGN=MIDDLE  ALT=\"sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >),(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2814%29 ALIGN=MIDDLE  ALT=\"-sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2814%29 ALIGN=MIDDLE  ALT=\"-sqrt%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2Ccircle%28sqrt%2810%29%2C0%2C0.3%29%2Ccircle%28-sqrt%2810%29%2C0%2C0.3%29%2C%0D%0Acircle%28sqrt%2814%29%2C2%2C0.3%29%2C%0D%0Acircle%28-sqrt%2814%29%2C2%2C0.3%29%2C%0D%0Acircle%28sqrt%2814%29%2C-2%2C0.3%29%2C%0D%0Acircle%28-sqrt%2814%29%2C-2%2C0.3%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2Ccircle%28sqrt%2810%29%2C0%2C0.3%29%2Ccircle%28-sqrt%2810%29%2C0%2C0.3%29%2C%0D%0Acircle%28sqrt%2814%29%2C2%2C0.3%29%2C%0D%0Acircle%28-sqrt%2814%29%2C2%2C0.3%29%2C%0D%0Acircle%28sqrt%2814%29%2C-2%2C0.3%29%2C%0D%0Acircle%28-sqrt%2814%29%2C-2%2C0.3%29%2C%0D%0Agraph%28300%2C300%2C-10%2C10%2C-10%2C10%2Csqrt%28x%5E2-10%29%2C-sqrt%28x%5E2-10%29%29%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );