document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=552062>Question 552062</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve,<BR>\n" );
document.write( "What is an equation for the hyperbola with vertices (3,0) and (-3,0) and asymptote y=4/3x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360135 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=360135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there's a lot to understand about hyperbolas that can be confusing.<BR>\n" );
document.write( "not having seen them in a while, i forgot most of what i had previously learned.<BR>\n" );
document.write( "a good reference to brush up on is:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/hyperbola.htm\">http://www.purplemath.com/modules/hyperbola.htm</a><BR>\n" );
document.write( "your problem states the following:<BR>\n" );
document.write( "vertices are (3,0) and (-3,0) and asymptote is given by the equation y = (4/3)x.<BR>\n" );
document.write( "this makes your hyperbola a horizontally aligned hyperbola.<BR>\n" );
document.write( "the formula for a horizontally aligned hyperbola is<BR>\n" );
document.write( "(x-h)^2/a^2 - (y-k)^2/b^2 = 1<BR>\n" );
document.write( "the center of this hyperbola will be halfway between the left vertex and the right vertex.<BR>\n" );
document.write( "that would be halfway between (-3,0) and (3,0) which is equal to (0,0).<BR>\n" );
document.write( "this makes h = 0 and k = 0 and the formula becomes:<BR>\n" );
document.write( "x^2/a^2 - y^2/b^2 = 1<BR>\n" );
document.write( "the formula for the asymptote is y = (4/3)x<BR>\n" );
document.write( "the general formula for the asymptote of a horizontally aligned hyperbola is:<BR>\n" );
document.write( "y = (b/a)(x-h)+k<BR>\n" );
document.write( "since h and k are both equal to 0, this becomes:<BR>\n" );
document.write( "y = (b/a)x<BR>\n" );
document.write( "we are given that y = (4/3)x.<BR>\n" );
document.write( "this makes:<BR>\n" );
document.write( "b = 4<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "our equation becomes:<BR>\n" );
document.write( "x^2/3^2 - y^2/4^2 = 1<BR>\n" );
document.write( "this simplifies to:<BR>\n" );
document.write( "x^2/9 - y^2/16 = 1<BR>\n" );
document.write( "if we multiply both sides of this equation by 144, we get:<BR>\n" );
document.write( "16x^2 - 9y^2 = 144<BR>\n" );
document.write( "add 9y^2 to both sides of this equation and subtract 144 from both sides of this equation to get:<BR>\n" );
document.write( "9y^2 = 16x^2 - 144<BR>\n" );
document.write( "divide both sides of this equation by 9 to get:<BR>\n" );
document.write( "y^2 = (16x^2-144)/9<BR>\n" );
document.write( "take the square root of both sides of this equation to get:<BR>\n" );
document.write( "y = +/- sqrt((16x^2-144)/9)<BR>\n" );
document.write( "graph both these equations as shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-20%2C20%2Csqrt%28%2816x%5E2-144%29%2F9%29%2C-sqrt%28%2816x%5E2-144%29%2F9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the equation for the asymptotes for this equation are:<BR>\n" );
document.write( "y = +/- (4/3)x<BR>\n" );
document.write( "add these to the graph to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-20%2C20%2Csqrt%28%2816x%5E2-144%29%2F9%29%2C-sqrt%28%2816x%5E2-144%29%2F9%29%2C%284%2F3%29x%2C-%284%2F3%29x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );