document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136818>Question 136818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the equation. Identify the conic section. Then find the domain and range.<BR>\n" );
document.write( "4x^2-24y^2-144=0. Please help me solve this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100140 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=100140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, let's see what kind of conic section you have by algebraic manipulation of your equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-24y%5E2-144+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2-24y%5E2-144+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 144 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-24y%5E2+=+144 ALIGN=MIDDLE  ALT=\"4x%5E2-24y%5E2+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide both sides by 144.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-24y%5E2%29%2F144+=+1 ALIGN=MIDDLE  ALT=\"%284x%5E2-24y%5E2%29%2F144+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F36%29-%28y%5E2%2F6%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F36%29-%28y%5E2%2F6%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Compare this with the standard form of an equation of a hyperbola with center (0, 0) and vertices on the x-axis:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Fa%5E2%29-%28y%5E2%2Fb%5E2%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Fa%5E2%29-%28y%5E2%2Fb%5E2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To graph this equation, you will need to solve it for y and, if done correctly, you will get a positive solution and a negative solution for y.<BR>\n" );
document.write( "You can then graph these two solutions to see the hyperbola.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F36%29-%28y%5E2%2F6%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F36%29-%28y%5E2%2F6%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F6+=+%28x%5E2%2F36%29-1 ALIGN=MIDDLE  ALT=\"y%5E2%2F6+=+%28x%5E2%2F36%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the right side then multiply both sides by 6.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+%28x%5E2-36%29%2F6 ALIGN=MIDDLE  ALT=\"y%5E2+=+%28x%5E2-36%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28%28x%5E2-36%29%2F6%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28%28x%5E2-36%29%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%28%28x%5E2-36%29%2F6%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%28%28x%5E2-36%29%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now graph these two equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-15%2C15%2C-5%2C5%2Csqrt%28%28x%5E2-36%29%2F6%29%2C-sqrt%28%28x%5E2-36%29%2F6%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The domain ( the set of all possible values of the independent variable (x)) is, as can be seen on the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%3Ex%3E6 ALIGN=MIDDLE  ALT=\"-6%3Ex%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The range (the set of all possible values of the dependent variable (y)) is:<BR>\n" );
document.write( "Y = all real numbers. </SPAN>\n" );
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