document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172563>Question 172563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, and directrix of the parabola given by x^2 - 6x - 12y - 15 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127463 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=127463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, and directrix of the parabola given by <BR>\n" );
document.write( "x^2 - 6x - 12y - 15 = 0<BR>\n" );
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document.write( "x^2 - 6x + ? = 12y + 15 + ?\r<BR>\n" );
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document.write( "x^2 -6x + 9 = 12y + 15 + 9\r<BR>\n" );
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document.write( "(x-3)^2 = 12(y + 2)<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Vertex: (3,-2)<BR>\n" );
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document.write( "Since 4p = 12, p = 3<BR>\n" );
document.write( "so the focus is at (3,-2+3) or (3,1)<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "directrix: x = 3<BR>\n" );
document.write( "======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );