document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135977>Question 1135977</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, directrix, and focal width of the parabola. <BR>\n" );
document.write( "x = 10y2<BR>\n" );
document.write( "choices are below<BR>\n" );
document.write( "Vertex: (0, 0); Focus: one divided by forty comma zero ; Directrix: x = negative one divided by forty ; Focal width: 0.1<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "Vertex: (0, 0); Focus: one divided by ten comma zero ; Directrix: x = negative one divided by ten ; Focal width: 0.1<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "Vertex: (0, 0); Focus: one divided by forty comma zero ; Directrix: x = one divided by forty ; Focal width: 40<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "Vertex: (0, 0); Focus: zero comma one divided by forty ; Directrix: y = negative one divided by forty ; Focal width: 40<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #753753 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=753753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "For me, the most useful form of the equation of a parabola (that opens right or left) is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-h+=+%281%2F%284p%29%29%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"x-h+=+%281%2F%284p%29%29%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In this form...<BR>\n" );
document.write( "(1) the vertex is (h,k);<BR>\n" );
document.write( "(2) p is the (directed) distance from the vertex to the focus; which means -p is the directed distance from the vertex to the directrix; and<BR>\n" );
document.write( "(3) 4p is the focal width (length of the latus rectum)<br><BR>\n" );
document.write( "Written in that form, the equation in your example is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-0+=+%281%2F%281%2F10%29%29%28y-0%29%5E2 ALIGN=MIDDLE  ALT=\"x-0+=+%281%2F%281%2F10%29%29%28y-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So...<BR>\n" );
document.write( "(1) the vertex is (0,0);<BR>\n" );
document.write( "(2) 4p=1/10 so p=1/40, so the focus is (1/40,0) and the directrix is x = -1/40; and<BR>\n" );
document.write( "(3) the focal width is 4p = 1/10 = 0.1<br><BR>\n" );
document.write( "The first answer choice is the correct one. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );