document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=723666>Question 723666</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the focus and directrix of the parabola with the equation y = 1/12x2? \r<BR>\n" );
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document.write( "focus: (3, 0) ; directrix: y = –3 <BR>\n" );
document.write( "focus: (–3, 0) ; directrix: y = 3<BR>\n" );
document.write( "focus: (0, 3) ; directrix: y = –3<BR>\n" );
document.write( "focus: (0, –3) ; directrix: y = 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443257 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443257\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard equation for a parabola with its axis vertical is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-h%29%5E2+=+4a%28y-k%29 ALIGN=MIDDLE  ALT=\"%28x+-h%29%5E2+=+4a%28y-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...(1)\r<BR>\n" );
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document.write( "The vertex is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k ALIGN=MIDDLE  ALT=\"+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "The focus is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+%2B+a ALIGN=MIDDLE  ALT=\"+k+%2B+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >).<BR>\n" );
document.write( "The directrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k+-a ALIGN=MIDDLE  ALT=\"y+=+k+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F12%29x%5E2+ ALIGN=MIDDLE  ALT=\"y+=+%281%2F12%29x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2F%281%2F12%29=+x%5E2+ ALIGN=MIDDLE  ALT=\"y+%2F%281%2F12%29=+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12y+=+x%5E2 ALIGN=MIDDLE  ALT=\"12y+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ....write it in form given above\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28y-0%29+=+%28x-0%29%5E2+ ALIGN=MIDDLE  ALT=\"12%28y-0%29+=+%28x-0%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0 ALIGN=MIDDLE  ALT=\"k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a=12 ALIGN=MIDDLE  ALT=\"4a=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3 ALIGN=MIDDLE  ALT=\"a=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "than,<BR>\n" );
document.write( "the vertex is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k ALIGN=MIDDLE  ALT=\"+k\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "the focus is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+%2B+a ALIGN=MIDDLE  ALT=\"k+%2B+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >)= (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%2B+3 ALIGN=MIDDLE  ALT=\"0+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3 ALIGN=MIDDLE  ALT=\"+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "the directrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+k+-a ALIGN=MIDDLE  ALT=\"y+=+k+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0-3 ALIGN=MIDDLE  ALT=\"y+=+0-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >...=>..<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=-3 ALIGN=MIDDLE  ALT=\"y+=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, your answer is: \r<BR>\n" );
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document.write( "focus: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3 ALIGN=MIDDLE  ALT=\"+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) ; directrix: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=-3 ALIGN=MIDDLE  ALT=\"y+=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28+600%2C+600%2C+-5%2C+5%2C+-5%2C5%2C+circle%280%2C3%2C.1%29%2Cgraph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C+%281%2F12%29x%5E2%2C-3%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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