document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878926>Question 878926</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Derive the equation of the parabola with a focus at (2, &#8722;1) and a directrix of y = &#8722;one half. Write in standard form.\r<BR>\n" );
document.write( "\n" );
document.write( "I got as far as finding a by graphing the focus and directrix to find the vertex then I found the focal length. Which is .25=p and by putting it into the equation for a=1/(4p. So I know a is equal to one but I am having trouble figuring out how to do the rest of the problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #530394 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=530394\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> focus at (2, &#8722;1) and a directrix of y = -1/2<BR>\n" );
document.write( "This tells us the parabola opens downward as directrix is above focus<BR>\n" );
document.write( "also tells us the V(2, -3/4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1-1%2F2%29%2F2+=+-3%2F4 ALIGN=MIDDLE  ALT=\"%28-1-1%2F2%29%2F2+=+-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > where p = -1/4<BR>\n" );
document.write( "a = 1/(4p), a = 1/(4(-1/4)) = -1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+-%28x-2%29%5E2+-3%2F4 ALIGN=MIDDLE  ALT=\"y=+-%28x-2%29%5E2+-3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the Vertex form, Standard Form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2+=+-%28y%2B3%2F4%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2+=+-%28y%2B3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the vertex form of a Parabola opening up(a>0) or down(a<0), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2+%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2+%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "where(h,k) is the vertex  and  x = h  is the Line of Symmetry<BR>\n" );
document.write( " a = 1/(4p), where  the focus is (h,k + p)and Directrix y = (k - p)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C+++-6%2C+6%2C+-6%2C+6%2C+grid%281%29%2C+blue%28line%282%2C6%2C2%2C-6%29%29+%2C%0D%0Acircle%282%2C+-.75%2C0.2%29%2C%0D%0Acircle%282%2C+-1%2C0.2%29%2C%0D%0Agraph%28+300%2C+300%2C+-6%2C+6%2C+-6%2C+6%2C0%2C+-.5%2C+-%28x-2%29%5E2+-3%2F4%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );