document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724506>Question 724506</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to know how to state whether certain graphs of an equation are a parabola, an ellipse, or a hyperbola. Some equations I'm given to determine these are:\r<BR>\n" );
document.write( "\n" );
document.write( "(number)=exponent\r<BR>\n" );
document.write( "\n" );
document.write( "1. y(2)+5=4(x+y)<BR>\n" );
document.write( "2. 2x(2)=8x-y(2)<BR>\n" );
document.write( "3. 4(y+1)(y-1)+5x(2)=24\r<BR>\n" );
document.write( "\n" );
document.write( "Please and thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443956 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=443956\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. y(2)+5=4(x+y)<BR>\n" );
document.write( "y^2+5=4x+4y<BR>\n" );
document.write( "y^2-4y=4x-5<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "(y^2-4y+4)=4x-5+4<BR>\n" );
document.write( "(y-2)^2=4x-1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%5E2=4%28x-1%2F4%29 ALIGN=MIDDLE  ALT=\"%28y-2%29%5E2=4%28x-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of a parabola that opens rightward<BR>\n" );
document.write( "Its basic form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-k%29%5E2=4p%28x-h%29 ALIGN=MIDDLE  ALT=\"%28y-k%29%5E2=4p%28x-h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (h,k)=(x,y) coordinates of the vertex<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2. 2x(2)=8x-y(2)<BR>\n" );
document.write( "2x^2+8x+y^2=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "2(x^2+4x+4)+y^2=0+8<BR>\n" );
document.write( "2(x+2)^2+y^2=8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%2F4%2By%5E2%2F8=1 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2F4%2By%5E2%2F8=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=%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=(x,y) coordinates of the center<BR>\n" );
document.write( "..<BR>\n" );
document.write( "3. 4(y+1)(y-1)+5x(2)=24<BR>\n" );
document.write( "4(y^2-1)+5x^2=24<BR>\n" );
document.write( "4y^2-4+5x^2=24<BR>\n" );
document.write( "4y^2+5x^2=24+4<BR>\n" );
document.write( "4y^2+5x^2=28<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F7%2Bx%5E2%2F%2828%2F5%29=1 ALIGN=MIDDLE  ALT=\"y%5E2%2F7%2Bx%5E2%2F%2828%2F5%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is an equation of an ellipse with horizontal major axis<BR>\n" );
document.write( "Its standard form: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a>b, (h,k)=(x,y) coordinates of the center </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );