document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=481497>Question 481497</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the focus and directrix of each parabola with the given equation.  \r<BR>\n" );
document.write( "\n" );
document.write( "   a).   x^=4y<BR>\n" );
document.write( "   <BR>\n" );
document.write( "   b).   y^=-4x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329844 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=329844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the focus and directrix of each parabola with the given equation. <BR>\n" );
document.write( "a). x^=4y<BR>\n" );
document.write( "b). y^=-4x<BR>\n" );
document.write( "**<BR>\n" );
document.write( "a). x^2=4y<BR>\n" );
document.write( "This is an equation of a parabola with a vertical axis of symmetry. <BR>\n" );
document.write( "Its standard form: (x-h)^2=4p(y-k), with (h,k) being the (x,y) coordinates of the vertex.<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "parabola opens upwards<BR>\n" );
document.write( "Vertex(0,0) <BR>\n" );
document.write( "4p=4<BR>\n" );
document.write( "p=1<BR>\n" );
document.write( "Focus:(0,1)<BR>\n" );
document.write( "Directrix: y=-1<BR>\n" );
document.write( "see the graph below as a visual check on the answers:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=±x^2/4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2F4%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "b). y^2=-4x<BR>\n" );
document.write( "This is an equation of a parabola with a horizontal axis of symmetry. <BR>\n" );
document.write( "Its standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "parabola opens leftward<BR>\n" );
document.write( "Vertex(0,0) <BR>\n" );
document.write( "4p=4<BR>\n" );
document.write( "p=1<BR>\n" );
document.write( "Focus:(-1,0)<BR>\n" );
document.write( "Directrix: x=1<BR>\n" );
document.write( "see the graph below as a visual check on the answers:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=±(-4x)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%28-4x%29%5E.5%2C-%28-4x%29%5E.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%28-4x%29%5E.5%2C-%28-4x%29%5E.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );