document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=853215>Question 853215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the equations below is for an ellipse and which is for a hyperbola?<BR>\n" );
document.write( "Demonstrate by explaining or showing how you can tell the difference without using a graphing<BR>\n" );
document.write( "calculator. You may use the coordinate plane below for sketching, if you choose.<BR>\n" );
document.write( "a) 4y2 = 144 + 16x2<BR>\n" );
document.write( "b) 4y2 + 16x2 = 144 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #513997 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=513997\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Which of the equations below is for an ellipse and which is for a hyperbola?<BR>\n" );
document.write( "Demonstrate by explaining or showing how you can tell the difference without using a graphing<BR>\n" );
document.write( "calculator. You may use the coordinate plane below for sketching, if you choose.<BR>\n" );
document.write( "a) 4y2 = 144 + 16x2<BR>\n" );
document.write( "4y^2-16x^2=144<BR>\n" );
document.write( "divide by 144<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F36-x%5E2%2F9=1 ALIGN=MIDDLE  ALT=\"y%5E2%2F36-x%5E2%2F9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of a hyperbola with vertical transverse axis.<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (h,k)=coordinates of center.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b) 4y2 + 16x2 = 144<BR>\n" );
document.write( "divide by 144<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F36%2Bx%5E2%2F9=1 ALIGN=MIDDLE  ALT=\"y%5E2%2F36%2Bx%5E2%2F9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of an ellipse with vertical major axis.<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2%2Fa%5E2%2B%28x-h%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2%2Fa%5E2%2B%28x-h%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (h,k)=coordinates of center.<BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );