document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138308>Question 1138308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ± 1 divided by 4 x. (5 points)<BR>\n" );
document.write( "	<BR>\n" );
document.write( "y squared over 16 minus x squared over 64 = 1<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "y squared over 16 minus x squared over 256 = 1<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "y squared over 256 minus x squared over 16 = 1<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "y squared over 64 minus x squared over 4 = 1<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756139 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " Find an equation in standard form for the hyperbola with vertices at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "\n" );
document.write( "and asymptotes at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y ALIGN=MIDDLE  ALT=\"+y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29+x ALIGN=MIDDLE  ALT=\"%281%2F4%29+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard form:\r<BR>\n" );
document.write( "\n" );
document.write( "since the vertices are at (0, ±4), that means the parabola opens up and down, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+4 ALIGN=MIDDLE  ALT=\"a+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the distance from center to vertex)\r<BR>\n" );
document.write( "\n" );
document.write( "the center will be halfway between the vertices at:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "\n" );
document.write( "the hyperbola will look like:\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2+%2F+a%5E2+-+%28x-h%29%5E2+%2F+b%5E2+=+1++++ ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2+%2F+a%5E2+-+%28x-h%29%5E2+%2F+b%5E2+=+1++++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-0%29%5E2+%2F+4%5E2+-+%28x-0%29%5E2+%2F+b%5E2+=+1++++ ALIGN=MIDDLE  ALT=\"%28y-0%29%5E2+%2F+4%5E2+-+%28x-0%29%5E2+%2F+b%5E2+=+1++++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+%2F+16+-+x%5E2+%2F+b%5E2+=+1++++ ALIGN=MIDDLE  ALT=\"y%5E2+%2F+16+-+x%5E2+%2F+b%5E2+=+1++++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "since given asymptotes at  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29+x+ ALIGN=MIDDLE  ALT=\"%281%2F4%29+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the slope of the vertices will be ± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb ALIGN=MIDDLE  ALT=\"a%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we have\r<BR>\n" );
document.write( "\n" );
document.write( "± <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2Fb+ ALIGN=MIDDLE  ALT=\"+4%2Fb+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+16 ALIGN=MIDDLE  ALT=\"b+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "substituting in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+16 ALIGN=MIDDLE  ALT=\"b+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > : \r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+%2F+16+-+x%5E2+%2F+16%5E2+=+1++++ ALIGN=MIDDLE  ALT=\"y%5E2+%2F+16+-+x%5E2+%2F+16%5E2+=+1++++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+%2F+16+-+x%5E2+%2F+256=+1+ ALIGN=MIDDLE  ALT=\"y%5E2+%2F+16+-+x%5E2+%2F+256=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );