document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=546364>Question 546364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for x - 4 = ( y + 5 ) ^2<BR>\n" );
document.write( "would (4,-5) be the vertex?<BR>\n" );
document.write( "and what is the focus and directrix?\r<BR>\n" );
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document.write( "also, what is the focus and directrix of -3( y +3)^2 = - (x+4) and -3 (x+2)^2 = - (y+6)\r<BR>\n" );
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document.write( "I was confused because I wasn't sure what the point was so I couldn't figure out the focus and directrix. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357013 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=357013\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for x - 4 = ( y + 5 ) ^2<BR>\n" );
document.write( "would (4,-5) be the vertex?<BR>\n" );
document.write( "and what is the focus and directrix? <BR>\n" );
document.write( "also, what is the focus and directrix of -3( y +3)^2 = - (x+4) and -3 (x+2)^2 = - (y+6) <BR>\n" );
document.write( "I was confused because I wasn't sure what the point was so I couldn't figure out the focus and directrix.<BR>\n" );
document.write( "**<BR>\n" );
document.write( "The following are 4 standard forms of equations for parabolas showing focus and directrix: <BR>\n" );
document.write( "(axis of symmetry vertical or horizontal)<BR>\n" );
document.write( "(x-h)^2=4p(y-k),  (h,k)=(x,y) of vertex, parabola opens upward)<BR>\n" );
document.write( "(x-h)^2=-4p(y-k),  (h,k)=(x,y) of vertex, parabola opens downward)<BR>\n" );
document.write( "(y-k)^2=4p(x-h),  (h,k)=(x,y) of vertex, (parabola opens rightward)<BR>\n" );
document.write( "(y-k)^2=-4p(x-h),  (h,k)=(x,y) of vertex, (parabola opens leftward)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given equation, x - 4 = ( y + 5 ) ^2, it could be rewritten: (y+5)^2=(x-4), which looks like the third form listed above. In this case, 4p=1, so p=1/4. The focus and directrix are p units from the vertex on the axis of symmetry. You are correct in saying the vertex is (4,-5).<BR>\n" );
document.write( "axis of symmetry: y=-5<BR>\n" );
document.write( "focus: (4+1/4,-5)=(17/4,-5)<BR>\n" );
document.write( "directrix: x=4-1/4=15/4<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given equation, -3( y +3)^2 = - (x+4), it could be rewritten: (y+3)^2=(1/3)(x+4), which also looks like the third form listed above. In this case, however, 4p=1/3, so p=1/12.  The focus and directrix are p units from the vertex on the axis of symmetry. <BR>\n" );
document.write( "vertex: (-4,-3).<BR>\n" );
document.write( "axis of symmetry: y=-3<BR>\n" );
document.write( "focus: (-4+1/12,-3)=(-47/12,-3)<BR>\n" );
document.write( "directrix: x=-4-1/12=-49/12<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For given equation, -3 (x+2)^2 = - (y+6), it could be rewritten: (x+2)^2=(1/3)(y+6), which looks like the first form listed above. In this case, 4p=1/3, so p=1/12.  The focus and directrix are p units from the vertex on the axis of symmetry.<BR>\n" );
document.write( "vertex: (-2,-6).<BR>\n" );
document.write( "axis of symmetry: x=-2<BR>\n" );
document.write( "focus: (-2,-6+1/12)=(-2,-71/12)<BR>\n" );
document.write( "directrix: y=-73/12\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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