document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136851>Question 1136851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I am having a very tough time with the conic sections portion of my algebra class. Is there anyway someone can help me solve the equation:\r<BR>\n" );
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document.write( "Find an equation for the hyperbola with vertices at (0, -6) and (0, 6); asymptote the line  y=3/5x\r<BR>\n" );
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document.write( "any help would be sincerely grateful!<BR>\n" );
document.write( "Thank you in advance for any help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754674 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Clearly there are two asymptotes; if the equation of one of them is y=(3/5)x, then the equation of the other is y = (-3/5)x.<br><BR>\n" );
document.write( "The coordinates of the vertices, and also the fact that the asymptotes pass through the origin, tell us that the center of the hyperbola is at the origin.<br><BR>\n" );
document.write( "And the vertices on the y-axis tell us that the branches of the hyperbola open up and down.<br><BR>\n" );
document.write( "The standard form of the equation of a hyperbola with center at the origin and branches opening up and down is<br><BR>\n" );
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document.write( "a is the distance from the center to each vertex, so you know a; all you need to finish the equation is b.<br><BR>\n" );
document.write( "For that, use the fact that the slopes of the asymptotes are a/b and -a/b.<BR>\n" );
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