document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982925>Question 982925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of the parabola with given vertex at the origin and directrix: 3x=-4  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603720 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=603720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The directrix given can be expressed  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2F3 ALIGN=MIDDLE  ALT=\"x=-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and y is unrestricted.  This parabola has axis of symmetry being the x-axis, and since this directrix is to the left of the vertex(the origin), the parabola is concave to the right.\r<BR>\n" );
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document.write( "Using the equation of form which comes from deriving from the definition of a parabola,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4py=x%5E2 ALIGN=MIDDLE  ALT=\"4py=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and because the distance from your directrix and the vertex is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-4%2F3%29=4%2F3 ALIGN=MIDDLE  ALT=\"abs%28-4%2F3%29=4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this determines <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28p=4%2F3%29 ALIGN=MIDDLE  ALT=\"highlight_green%28p=4%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Substitute for p into the derived equation form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%284%2F3%29x=y%5E2 ALIGN=MIDDLE  ALT=\"4%284%2F3%29x=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifiable to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%2816%2F3%29x=y%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28%2816%2F3%29x=y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can also derive the equation for your description using your given directrix  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4%2F3 ALIGN=MIDDLE  ALT=\"x=-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and the focus 4/3 units to the right of the vertex ; the focus which is  ( 4/3, 0), using the definition and Distance Formula. </SPAN>\n" );
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