document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=772845>Question 772845</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the focus of the conic section 12x+y^2-14y+1=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471404 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=471404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what is the focus of the conic section <BR>\n" );
document.write( "12x+y^2-14y+1=0<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "(y^2-14y+49)-49+1=-12x<BR>\n" );
document.write( "(y^2-14y+49)-48=-12x<BR>\n" );
document.write( "(y^2-7)^2=-12x+48<BR>\n" );
document.write( "(y^2-7)^2=-12(x-4)<BR>\n" );
document.write( "This is an equation of a parabola that opens leftward:<BR>\n" );
document.write( "Its basic equation: (y-k)^2=-4p(x-h), (h,k)=(x,y) coordinates of the vertex<BR>\n" );
document.write( "For given parabola:<BR>\n" );
document.write( "vertex: (4,7)<BR>\n" );
document.write( "axis of symmetry: y=7<BR>\n" );
document.write( "4p=12<BR>\n" );
document.write( "p=3<BR>\n" );
document.write( "focus: (1,7) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );