document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=600372>Question 600372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem:  3yy+24y-xx-2x+41=0<BR>\n" );
document.write( "have to decide if it is a circle, ellipse, parabola, or hyperbola.<BR>\n" );
document.write( "it it is a hyperbola the equation has to be in this form:<BR>\n" );
document.write( "(x-h)(x-h)/aa-(y-k)(y-k)/bb=1    or      (y-k)(y-k)/aa-(x-h)(x-h)/bb=1<BR>\n" );
document.write( "Parabola: y=a(x-h)(x-h)+k    or     x=a(y-k)(y-k)+h<BR>\n" );
document.write( "then graph please. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379392 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=379392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem: 3yy+24y-xx-2x+41=0<BR>\n" );
document.write( "have to decide if it is a circle, ellipse, parabola, or hyperbola.<BR>\n" );
document.write( "it it is a hyperbola the equation has to be in this form:<BR>\n" );
document.write( "(x-h)(x-h)/aa-(y-k)(y-k)/bb=1 or (y-k)(y-k)/aa-(x-h)(x-h)/bb=1<BR>\n" );
document.write( "Parabola: y=a(x-h)(x-h)+k or x=a(y-k)(y-k)+h<BR>\n" );
document.write( "then graph please<BR>\n" );
document.write( "**<BR>\n" );
document.write( "3y^2+24y-x^2-2x+41=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "3(y^2+8y+16)-(x^2+2x+1)=-41+48-1<BR>\n" );
document.write( "3(y+4)^2-(x+1)^2=6<BR>\n" );
document.write( "divide by 6<BR>\n" );
document.write( "(y+4)^2/2-(x+1)^2/6=1<BR>\n" );
document.write( "This is an equation of a hyperbola with vertical transverse axis (y-term listed first)<BR>\n" );
document.write( "Its standard form: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "center: (-1,-4)<BR>\n" );
document.write( "a^2=2<BR>\n" );
document.write( "a=&#8730;2<BR>\n" );
document.write( "length of vertical transverse axis=2a=2&#8730;2&#8776;2.83<BR>\n" );
document.write( "b^2=6<BR>\n" );
document.write( "b=&#8730;6<BR>\n" );
document.write( "length of conjugate axis=2b=2&#8730;6&#8776;4.9<BR>\n" );
document.write( "see graph below<BR>\n" );
document.write( "y=(2+(x+1)^2/3)^.5-4\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );