document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750606>Question 750606</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write an equation of the conic/parabola with vertex at (-4,3) and focus at (-4,-2). I'm having trouble with this section of math and it would be great if you could help me. thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456724 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=456724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The focal length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283-%28-2%29%29=5 ALIGN=MIDDLE  ALT=\"abs%283-%28-2%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You should reread the book discussion about deriving the equation for a parabola.  if p is the focal length, then a standard position parabola is <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;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F%284p%29%29x%5E2 ALIGN=MIDDLE  ALT=\"y=%281%2F%284p%29%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "You should use the standard form for a parabola, since you know your vertex, as given (-4,3).  Putting this information into the standard form equation, you have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F%284p%29%29%28x%2B4%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"y=%281%2F%284p%29%29%28x%2B4%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and because you know p=5, the focal length,<BR>\n" );
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document.write( "You can leave in standard form, or you can multiply and simplify the right hand side into general form.  \r<BR>\n" );
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document.write( "*____Note that the standard form equation for a parabola is <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;\" >  where the vertex is (h,k). </SPAN>\n" );
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