document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049488>Question 1049488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this question.\r<BR>\n" );
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document.write( "Find an equation for the hyperbola that satisfies the given conditions:\r<BR>\n" );
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document.write( "12. Vertices (0, ±4), asymptotes y = ± 1/2x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #665116 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=665116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Vertices (0, ±4), asymptotes y = ± 1/2x<BR>\n" );
document.write( "OPens Up an Down<BR>\n" );
document.write( "Standard Form of an Equation of an Hyperbola opening up and down is:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis<BR>\n" );
document.write( "Foci <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >units units up and down from center, along x = h<BR>\n" );
document.write( "& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a<BR>\n" );
document.write( "Vertices (0, ±4) therefore C(0,0)<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%29%5E2%2F4%5E2+-+%28x%29%5E2%2Fa%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28y%29%5E2%2F4%5E2+-+%28x%29%5E2%2Fa%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "asymptotes y = ± 1/2x<BR>\n" );
document.write( "m = ± b/a <BR>\n" );
document.write( "4/a = 1/2<BR>\n" );
document.write( "a = 8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%29%5E2%2F4%5E2+-+%28x%29%5E2%2F8%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28y%29%5E2%2F4%5E2+-+%28x%29%5E2%2F8%5E2+=+1\"   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-20%2C20%2C-20%2C20%2C+blue%28line%280%2C10%2C0%2C-10%29%29%2C%0D%0A+grid%281%29%2C%0D%0Acircle%280%2C0%2C0.4%29%2C%0D%0Acircle%280%2C+-4%2C0.4%29%2C%0D%0Acircle%280%2C+4%2C0.4%29%2C%0D%0A%0D%0Agraph%28+300%2C+300%2C-20%2C20%2C-20%2C20%2C0%2C+.5x%2C+-.5x%2C+4sqrt%28%28x%29%5E2%2F64+%2B+1%29%2C-4sqrt%28%28x%29%5E2%2F64+%2B1+%29++%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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