document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119528>Question 1119528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the focus, vertex, length of latus rectum,and the equation of directrix of the parabola y^2 - 10x = 0 </SPAN>\n" );
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document.write( "The equation has a y^2 term, so the parabola opens right or left.  Vertex form for 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( "where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.<br><BR>\n" );
document.write( "Note with this form of the equation, the length of the latus rectum (perpendicular to the axis of symmetry and through the focus) is |4p|.<br><BR>\n" );
document.write( "Put the given equation in that form:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-10x+=+0 ALIGN=MIDDLE  ALT=\"y%5E2-10x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x+=+y%5E2 ALIGN=MIDDLE  ALT=\"10x+=+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F10%29y%5E2 ALIGN=MIDDLE  ALT=\"x+=+%281%2F10%29y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-0+=+%281%2F10%29%28y-0%29%5E2 ALIGN=MIDDLE  ALT=\"x-0+=+%281%2F10%29%28y-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This is in vertex form.  The vertex is (0,0); p = 10/4 = 2.5.<br><BR>\n" );
document.write( "vertex: (0,0)<BR>\n" );
document.write( "focus: p = 2.5 right of the vertex, at (2.5,0)<BR>\n" );
document.write( "directrix: p = 2.5 left of the vertex; x = -2.5<BR>\n" );
document.write( "length of latus rectum: 4p = 10 </SPAN>\n" );
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