document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=54271>Question 54271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the vertex, focus, directrix of the parabola by x^2 -4x -6y -16 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #36525 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=36525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> find the vertex, focus, directrix of the parabola by x^2 -4x -6y -16 = 0<BR>\n" );
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document.write( "Rewrite as:<BR>\n" );
document.write( "x^2-4x+? = 6y+16+?<BR>\n" );
document.write( "Complete the square:<BR>\n" );
document.write( "x^2-4x+4=6y+16+4<BR>\n" );
document.write( "(x-2)^2 = 6(y+(10/3))<BR>\n" );
document.write( "This follows the form (x-h)^2=4p(y-k)<BR>\n" );
document.write( "h=2; k=-10/3; p=3/2<BR>\n" );
document.write( "Vertex at (2,10/3); focus=(2,(10/3)+(3/2))=(2,29/6);<BR>\n" );
document.write( "directrix: y = (10/3)-(3/2)=11/6<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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