document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43057>Question 43057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"Graph the equation, then choose the correct coordinates of the foci. Keep the graphs as they may be asked for at a later time. y^2= 5x^2+25.\" I keep trying to graph equations like this and find the foci, but the answers I get are never one of the answer choices. For this one I did:<BR>\n" );
document.write( "y^2= 5x^2+25<BR>\n" );
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document.write( "y^2-5x^2= 25<BR>\n" );
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document.write( "(y^2-5x^2)/-5=25/-5\r<BR>\n" );
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document.write( "-1/5(y^2/-5-x^2)=-5/-5<BR>\n" );
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document.write( "y^2/25+x^2/5=1\r<BR>\n" );
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document.write( "y^2/(5)^2+x^2/(square root 5)^2=1\r<BR>\n" );
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document.write( "After that I had my x and y intercepts so I made my graph and tried to find the foci.\r<BR>\n" );
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document.write( "b^2=a^2-c^2\r<BR>\n" );
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document.write( "square root 5^2= 5^2-c^2\r<BR>\n" );
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document.write( "5= 25-c^2\r<BR>\n" );
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document.write( "5-25= -c^2\r<BR>\n" );
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document.write( "20= c^2\r<BR>\n" );
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document.write( "square root 20= c  <BR>\n" );
document.write( "I'd appreciate your help. These graphs have really been frustrating me. Please me know what I'm doing wrong. Thanx! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28077 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=28077\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=+5x%5E2%2B25 ALIGN=MIDDLE  ALT=\"y%5E2=+5x%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-5x%5E2=+25 ALIGN=MIDDLE  ALT=\"y%5E2-5x%5E2=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2-5x%5E2%29%2F25=25%2F25%29 ALIGN=MIDDLE  ALT=\"%28y%5E2-5x%5E2%29%2F25=25%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F25+-+x%5E2%2F5+=+1 ALIGN=MIDDLE  ALT=\"y%5E2%2F25+-+x%5E2%2F5+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F5%5E2+-+x%5E2%2F%28sqrt%285%29%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"y%5E2%2F5%5E2+-+x%5E2%2F%28sqrt%285%29%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As simple as that! <BR>\n" );
document.write( "Don't make the algebra complex. <BR>\n" );
document.write( "Divide both sides by 25 (to make the term on right side = 1).<BR>\n" );
document.write( "This is a hyperbola and not an ellipse.<BR>\n" );
document.write( "You derived a wrong equation resulting in wrong type of conic (you got ellipse).\r<BR>\n" );
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document.write( "Comparing with standard equation of hyperbola<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Fa%5E2+-+x%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"y%5E2%2Fa%5E2+-+x%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "where '2a' and '2b' are the lengths of transverse and conjugate axes respectively we have<BR>\n" );
document.write( "a = 5, b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, eccentricity is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=sqrt%281+%2B+b%5E2%2Fa%5E2%29 ALIGN=MIDDLE  ALT=\"e=sqrt%281+%2B+b%5E2%2Fa%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=sqrt%281+%2B+5%2F5%5E2%29 ALIGN=MIDDLE  ALT=\"e=sqrt%281+%2B+5%2F5%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=sqrt%281+%2B+1%2F5%29 ALIGN=MIDDLE  ALT=\"e=sqrt%281+%2B+1%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e=sqrt%286%2F5%29 ALIGN=MIDDLE  ALT=\"e=sqrt%286%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The foci are at (0,ae) and (0,-ae) i.e. (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5sqrt%286%2F5%29 ALIGN=MIDDLE  ALT=\"5sqrt%286%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5sqrt%286%2F5%29 ALIGN=MIDDLE  ALT=\"-5sqrt%286%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) i.e. (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2830%29 ALIGN=MIDDLE  ALT=\"sqrt%2830%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (0,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2830%29 ALIGN=MIDDLE  ALT=\"-sqrt%2830%29\"   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=graph%28600%2C600%2C-20%2C20%2C-20%2C20%2C+sqrt%285x%5E2%2B25%29%2C+-sqrt%285x%5E2%2B25%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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