document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145166>Question 145166</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertex, focus, and directrix of the parabola given by<BR>\n" );
document.write( "x^2-10x-8y+33=0\r<BR>\n" );
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document.write( "I think:<BR>\n" );
document.write( "x^2-10x=8y-33<BR>\n" );
document.write( "but I'm not sure what to do from there.\r<BR>\n" );
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document.write( "Please explain the steps to me if you can, thanks for your help!\r<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 #106029 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=106029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Good start.  You have correctly completed the first step.\r<BR>\n" );
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document.write( "Next step:  Complete the square on the x terms.  Divide the coefficient on the 1st degree x term by 2 and square it.  Add the result to both sides of the equation.  That will give you a perfect square on the left, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10x%2B25=8y-33%2B25 ALIGN=MIDDLE  ALT=\"x%5E2-10x%2B25=8y-33%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2=8%28y-1%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2=8%28y-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now your equation is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2=4p%28y-k%29 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2=4p%28y-k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a parabola with:<BR>\n" );
document.write( "Vertex at (h,k),<BR>\n" );
document.write( "Focus at (h,k+p), and<BR>\n" );
document.write( "Directrix y = k - p\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p=8 ALIGN=MIDDLE  ALT=\"4p=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <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;\" > and the focus is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >), the vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and the directrix is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-1 ALIGN=MIDDLE  ALT=\"y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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