document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170145>Question 170145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question states, write the standard equation for each conic given the following info. \r<BR>\n" );
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document.write( "Parabola with a focus (-2,3) and a directrix x=2\r<BR>\n" );
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document.write( "how do i write the standard equation with this given information?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125588 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=125588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First we need to find the vertex:\r<BR>\n" );
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document.write( "X-coordinate of the vertex: Simply average the x coordinate of the focus (-2) with the directix (2) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2%2B2%29%2F2=0%2F2=0 ALIGN=MIDDLE  ALT=\"%28-2%2B2%29%2F2=0%2F2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the x-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Y-coordinate of the vertex: This value is equal to the y-coordinate of the focus. So the y-coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3 ALIGN=MIDDLE  ALT=\"y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the vertex is (0,3)\r<BR>\n" );
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document.write( "Now that we have the vertex, we can use that to find the distance from the focus to the vertex.\r<BR>\n" );
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document.write( "Since the focus (-2,3) is 2 units from the vertex (0,3), this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2 ALIGN=MIDDLE  ALT=\"p=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's find the equation:\r<BR>\n" );
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document.write( "Since the focus is (-2,3) and the directrix is x=2, this means that the parabola is opening to the left like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/parabola.png\" alt=\"Photobucket - Video and Image Hosting\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4p%28x-h%29=%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"-4p%28x-h%29=%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the standard equation (for parabolas that open up to the left)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%282%29%28x-0%29=%28y-3%29%5E2 ALIGN=MIDDLE  ALT=\"-4%282%29%28x-0%29=%28y-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=2 ALIGN=MIDDLE  ALT=\"p=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%28x-0%29=%28y-3%29%5E2 ALIGN=MIDDLE  ALT=\"-8%28x-0%29=%28y-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So the standard equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%28x-0%29=%28y-3%29%5E2 ALIGN=MIDDLE  ALT=\"-8%28x-0%29=%28y-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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