document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617191>Question 617191</A>: <I><SPAN STYLE=\"word-break: break-all;\">          <BR>\n" );
document.write( "(y+1)^2    = 12(x-1)\r<BR>\n" );
document.write( "\n" );
document.write( "Graph, including the foci </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388204 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20059)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=388204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (y + 1)² = 12(x - 1)\r<BR>\n" );
document.write( "\n" );
document.write( "Graph, including the foci.<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "We<BR>\n" );
document.write( "(y - k)² = 4p(x - h)\r<BR>\n" );
document.write( "\n" );
document.write( "has vertex (h,k).  If p is positive it opens to the right.<BR>\n" );
document.write( "If p is negative it opens to the left. its fccus is inside<BR>\n" );
document.write( "the parabola on its axis on symmetry and |p| units from the<BR>\n" );
document.write( "vertex.And the latus rectum or focal chord is |4p| units long<BR>\n" );
document.write( "bisected by the focus.\r<BR>\n" );
document.write( "\n" );
document.write( "Comparing your equation to that, we get\r<BR>\n" );
document.write( "\n" );
document.write( "h=1, k= -1, 4p=12, so p=3\r<BR>\n" );
document.write( "\n" );
document.write( "So the graph opens to the right because p is positive\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C800%2C-2%2C7%2C-10%2C9%2C%0D%0Ared%28arc%287%2C-1%2C-12%2C12%2C90%2C270%29%29%2Clocate%284%2C-1%2C%22FOCUS_%284%2C-1%29%22%29%2C%0D%0Agraph%28400%2C800%2C-2%2C7%2C-10%2C9%2Csqrt%2812%28x-1%29%29-1%29%2C+circle%284%2C-1%2C.1%29%2C%0D%0A%0D%0Agraph%28400%2C800%2C-2%2C7%2C-10%2C9%2C-sqrt%2812%28x-1%29%29-1%29++%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An the focus is a point inside the parabola |p| or 3 units<BR>\n" );
document.write( "to the right of the vertex.  The vertex is (1,-1), so the <BR>\n" );
document.write( "focus is (4,-1) \r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );