document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154307>Question 154307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Convert the equation to standard form by completing the square on x or y. Then find the vertex, focus?<BR>\n" );
document.write( "and directrix of the parabola. \r<BR>\n" );
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document.write( "Please show work so I know you got your answer and I can learn, please.\r<BR>\n" );
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document.write( "1. x^2+6x+8y+1=0\r<BR>\n" );
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document.write( "2. y^2-2y-8x+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 #113633 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><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=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=113633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> one general form of the equation of a parabola is (x-h)^2=4p(y-k)<BR>\n" );
document.write( "__ (the x and y may be switched, depending on the direction of the parabola)<BR>\n" );
document.write( "__ the vertex is (h,k), and p is the distance from the vertex to the focus<BR>\n" );
document.write( "__ since the vertex is midway between the focus and directrix, -p is the distance from the vertex to the directrix<BR>\n" );
document.write( "__ the vertex and focus are on the axis of symmerty, the directrix is perpendicular to the axis\r<BR>\n" );
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document.write( "so, the \"trick\" is to manipulate the equation until it looks like the general form\r<BR>\n" );
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document.write( "x^2+6x+8y+1=0 __ subtracting 8y+1 __ x^2+6x=-8y-1 __ completing the square by adding (6/2)^2 (from 6x) __ x^2+6x+9=-8y-1+9\r<BR>\n" );
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document.write( "x^2+6x+9=-8y+8 __ factoring __ (x+3)^2=-8(y-1)<BR>\n" );
document.write( "__ vertex is (-3,1)<BR>\n" );
document.write( "__ focus is (-3,-1)<BR>\n" );
document.write( "__ directrix is y=3\r<BR>\n" );
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document.write( "y^2-2y-8x+1=0 __ subtracting -8x+1 __ y^2-2y=8x-1 __ completing the square by adding (-2/2)^2 __ y^2-2y+1=8x-1+1\r<BR>\n" );
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document.write( "y^2-2x+1=8x __ factoring __ (y-1)^2=8(x-0)<BR>\n" );
document.write( "__ vertex is (0,1)<BR>\n" );
document.write( "__ focus is (2,1)<BR>\n" );
document.write( "__ directrix is x=-2<BR>\n" );
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