document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119530>Question 1119530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, length of latus rectum,and the equation of directrix of y^2 - 4y + 4x = 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+-+4y+%2B+4x+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+-+4y+%2B+4x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-4y%2B4+%2B+4x+-4+=+0 ALIGN=MIDDLE  ALT=\"y%5E2-4y%2B4+%2B+4x+-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-4+=+-%28y%5E2-4y%2B4%29 ALIGN=MIDDLE  ALT=\"4x-4+=+-%28y%5E2-4y%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-1%29+=+-1%28y-2%29%5E2 ALIGN=MIDDLE  ALT=\"4%28x-1%29+=+-1%28y-2%29%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-1+=+%281%2F-4%29%28y-2%29%5E2 ALIGN=MIDDLE  ALT=\"x-1+=+%281%2F-4%29%28y-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br><BR>\n" );
document.write( "This is in vertex form.  The vertex is (1,2); p = -4/4 = -1.<br><BR>\n" );
document.write( "vertex: (1,2)<BR>\n" );
document.write( "focus: p = 1 left of the vertex; at (0,2)<BR>\n" );
document.write( "directrix: p = 1 right of the vertex; x = 2<BR>\n" );
document.write( "length of latus rectum: |4p| = 4 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );