document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553690>Question 553690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for the hyperbola with vertices (4,0) and (-4,0) and asymptote y=1/4x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360987 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=360987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> vertices are (4,0) and (-4,0).<BR>\n" );
document.write( "that makes this a horizontally aligned hyperbola.<BR>\n" );
document.write( "the center of the hyperbola is midway between the left and right vertex which makes the center equal to (0,0).<BR>\n" );
document.write( "the distance from the center to the foci of the hyperbola are called c and are given by the equation c^2 = sqrt(a^2 + b^2).<BR>\n" );
document.write( "a is the distance from the vertex to the center which is equal to 4.<BR>\n" );
document.write( "the equation for the asymptote of a horizontally aligned hyperbola is y = +/- (b/a) * x<BR>\n" );
document.write( "you are given that the equation of the asymptote is y = +/- (1/4)x.<BR>\n" );
document.write( "this makes b equal to 1 and a equal to 4.<BR>\n" );
document.write( "the formula for a horizontally aligned hyperbola is:<BR>\n" );
document.write( "x^2/a^2 - y^2/b^2 = 1 with c = sqrt(a^2 + b^2)<BR>\n" );
document.write( "this makes c = sqrt(16+1) = sqrt(17).<BR>\n" );
document.write( "this makes the foci at (-sqrt(17),0) and (sqrt(17),0)<BR>\n" );
document.write( "so far, the equation of your ellipse is:<BR>\n" );
document.write( "x^2/16 - y^2 = 1<BR>\n" );
document.write( "to graph this hyperbola, solve for y to get:<BR>\n" );
document.write( "y = +/- sqrt((x^2/16)-1)<BR>\n" );
document.write( "to graph the asymptotes, graph the equations of:<BR>\n" );
document.write( "y = +/- (1/4)x<BR>\n" );
document.write( "the graph will look like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Csqrt%28%28x%5E2%2F16%29-1%29%2C-sqrt%28%28x%5E2%2F16%29-1%29%2C%281%2F4%29x%2C-%281%2F4%29x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a more far out view is shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-20%2C20%2C-10%2C10%2Csqrt%28%28x%5E2%2F16%29-1%29%2C-sqrt%28%28x%5E2%2F16%29-1%29%2C%281%2F4%29x%2C-%281%2F4%29x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "i never remember the formulas and always have to go to the references to get the formula again.<BR>\n" );
document.write( "here's a reference i used this time.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://home.windstream.net/okrebs/page63.html\" target = \"_blank\">http://home.windstream.net/okrebs/page63.html</a><BR>\n" );
document.write( "the foci are not shown on the graph that is mechanically generated.<BR>\n" );
document.write( "if you have to show them, then you need to print out the graph and put them there manually.<BR>\n" );
document.write( "One of the distinguishing properties of a hyperbola is that the absolute value of the difference of the distance between any point on the hyperbola and the two foci of the hyperbola will be a constant.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );