document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=455752>Question 455752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of a hyperbola with the gicen characteristics. <BR>\n" );
document.write( "vertices (-5,3) and (-1,3), foci (-3-2 sqrt5,3) and (-3+2 sqrt5,3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #313750 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=313750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write the equation of a hyperbola with the gicen characteristics. <BR>\n" );
document.write( "vertices (-5,3) and (-1,3), foci (-3-2 sqrt5,3) and (-3+2 sqrt5,3)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of a hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form of a hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "The difference between the two forms is the interchange of (x-h) and (y-k)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Since the y-coordinates of the vertices and foci are the same at 3, given hyperbola has a horizontal transverse axis. This is also the y-coordinate of the center. The x-coordinate of the center is the midpoint of the vertices on the transverse axis(-5+(-1)/2=-6/2=-3)<BR>\n" );
document.write( "center at (-3,3)<BR>\n" );
document.write( "length of the transverse axis=4=2a<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "a^2=4<BR>\n" );
document.write( "c=distance from center to foci=2&#8730;5=4.47..<BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "b^2=c^2-a^2=(2&#8730;5)^2-4=20-4=16<BR>\n" );
document.write( "b=4<BR>\n" );
document.write( "Equation: (x+3)^2/4-(y-3)^2/16=1 (ans)<BR>\n" );
document.write( "Asymptotes:y=2x+9, y=-2x-3<BR>\n" );
document.write( "see graph below as a visual check on the algebra above.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=(4(x+3)^2-16)^.5+3\r<BR>\n" );
document.write( "\n" );
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