document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=737564>Question 737564</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hyperbolas: <BR>\n" );
document.write( "Graph each hyperbola. Identify the verices, foci, and asymptotes\r<BR>\n" );
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document.write( "X^2/4 - y^2/16 = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #450721 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=450721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph each hyperbola. Identify the verices, foci, and asymptotes <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4+-+y%5E2%2F16+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4+-+y%5E2%2F16+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a hyperbola that has a horizontal transverse axis (x-term listed first ahead of y-term)<BR>\n" );
document.write( "Its standard form of equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For given hyperbola:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4+-+y%5E2%2F16+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F4+-+y%5E2%2F16+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "center: (0,0)<BR>\n" );
document.write( "a^2=4<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "vertices: (0±a,0)=(0±2,0)=(-2,0) and (2,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=16<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c^2=a^2+b^2=4+16=20<BR>\n" );
document.write( "c=&#8730;20&#8776;4.47<BR>\n" );
document.write( "foci: (0±c,0)=(0±4.47,0)=(-4.47,0) and (4.47,0)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Asymptotes: (equations of lines that go thru center, y=mx+b, m=slope, b= y-intercept)<BR>\n" );
document.write( "Slopes of asymptotes of hyperbolas with horizontal transverse axis=±b/a=±4/2=±2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with negative slope=-2<BR>\n" );
document.write( "y=-2x+b<BR>\n" );
document.write( "b=0<BR>\n" );
document.write( "y=-2x<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with positive slope=2<BR>\n" );
document.write( "y=2x+b<BR>\n" );
document.write( "b=0<BR>\n" );
document.write( "y=2x<BR>\n" );
document.write( "...<BR>\n" );
document.write( "y=±(4x^2-16)^.5<BR>\n" );
document.write( "See graph below as a visual check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%284x%5E2-16%29%5E.5%2C-%284x%5E2-16%29%5E.5%2C2x%2C-2x%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );