document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044782>Question 1044782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation <BR>\n" );
document.write( "Find the Parabola properties and graph<BR>\n" );
document.write( "y^2+6x+6y=39\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Vertex:<BR>\n" );
document.write( "Focus:<BR>\n" );
document.write( "Directrix:<BR>\n" );
document.write( "Axis of symmetry:<BR>\n" );
document.write( "Endpoints of latus retum:<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660184 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=660184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the Parabola properties and graph\r<BR>\n" );
document.write( "\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B6x%2B6y=39 ALIGN=MIDDLE  ALT=\"y%5E2%2B6x%2B6y=39\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Vertex:<BR>\n" );
document.write( "first write your equation in vertex form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-h=a%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"x-h=a%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since y squared) where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinates of the vertex<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=-y%5E2-6y%2B39 ALIGN=MIDDLE  ALT=\"6x=-y%5E2-6y%2B39\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-y%5E2%2F6-6y%2F6%2B39%2F6 ALIGN=MIDDLE  ALT=\"x=-y%5E2%2F6-6y%2F6%2B39%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%281%2F6%29%28y%5E2%2B6y%29%2B13%2F2 ALIGN=MIDDLE  ALT=\"x=-%281%2F6%29%28y%5E2%2B6y%29%2B13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%281%2F6%29%28y%5E2%2B6y%2Bb%5E2%29-%28-1%2F6%29b%5E2%2B13%2F2 ALIGN=MIDDLE  ALT=\"x=-%281%2F6%29%28y%5E2%2B6y%2Bb%5E2%29-%28-1%2F6%29b%5E2%2B13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%281%2F6%29%28y%5E2%2B6y%2B3%5E2%29-%28-1%2F6%293%5E2%2B13%2F2 ALIGN=MIDDLE  ALT=\"x=-%281%2F6%29%28y%5E2%2B6y%2B3%5E2%29-%28-1%2F6%293%5E2%2B13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%281%2F6%29%28y%2B3%29%5E2-%28-1%2F6%299%2B13%2F2 ALIGN=MIDDLE  ALT=\"x=-%281%2F6%29%28y%2B3%29%5E2-%28-1%2F6%299%2B13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%281%2F6%29%28y%2B3%29%5E2%2B3%2F2%2B13%2F2 ALIGN=MIDDLE  ALT=\"x=-%281%2F6%29%28y%2B3%29%5E2%2B3%2F2%2B13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%281%2F6%29%28y%2B3%29%5E2%2B16%2F2 ALIGN=MIDDLE  ALT=\"x=-%281%2F6%29%28y%2B3%29%5E2%2B16%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%281%2F6%29%28y%2B3%29%5E2%2B8 ALIGN=MIDDLE  ALT=\"x=-%281%2F6%29%28y%2B3%29%5E2%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8 ALIGN=MIDDLE  ALT=\"h=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "vertex is at ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   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;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "Since the value of a is negative, the parabola opens left.\r<BR>\n" );
document.write( "\n" );
document.write( "Focus: <BR>\n" );
document.write( "The focus of a parabola can be found by adding p to the x-coordinate h if the parabola opens left or right.<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Bp ALIGN=MIDDLE  ALT=\"h%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Find p, the distance from the vertex to the focus.\r<BR>\n" );
document.write( "\n" );
document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the distance from the vertex to a focus of the parabola by using the following formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1%2F4a ALIGN=MIDDLE  ALT=\"p=1%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1%2F6 ALIGN=MIDDLE  ALT=\"a=-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1%2F%284%28-1%2F6%29%29 ALIGN=MIDDLE  ALT=\"p=1%2F%284%28-1%2F6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-6%2F4 ALIGN=MIDDLE  ALT=\"p=-6%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-3%2F2 ALIGN=MIDDLE  ALT=\"p=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-3%2F2 ALIGN=MIDDLE  ALT=\"8-3%2F2\"   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;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F2-3%2F2 ALIGN=MIDDLE  ALT=\"16%2F2-3%2F2\"   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;\" >)\r<BR>\n" );
document.write( "\n" );
document.write( " ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2 ALIGN=MIDDLE  ALT=\"13%2F2\"   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;\" >)->focus\r<BR>\n" );
document.write( "\n" );
document.write( "Directrix:<BR>\n" );
document.write( "The directrix of a parabola is the vertical line found by subtracting p from the x-coordinate h<BR>\n" );
document.write( "of the vertex if the parabola opens left or right.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=h-p ALIGN=MIDDLE  ALT=\"x=h-p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8-%28-3%2F2%29 ALIGN=MIDDLE  ALT=\"x=8-%28-3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16%2F2%2B3%2F2 ALIGN=MIDDLE  ALT=\"x=16%2F2%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+19%2F2 ALIGN=MIDDLE  ALT=\"x+=+19%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Axis of symmetry:<BR>\n" );
document.write( "Find the axis of symmetry by finding the line that passes through the vertex and the focus.<BR>\n" );
document.write( "vertex is at ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   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;\" >)<BR>\n" );
document.write( " ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2 ALIGN=MIDDLE  ALT=\"13%2F2\"   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;\" >)->focus<BR>\n" );
document.write( "and that will be <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;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Endpoints of latus retum:\r<BR>\n" );
document.write( "\n" );
document.write( "length of latus rectum = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p=4%2A%28-3%2F2%29=2%28-3%29=-6 ALIGN=MIDDLE  ALT=\"4p=4%2A%28-3%2F2%29=2%28-3%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "endpoints of the latus rectum:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Bp ALIGN=MIDDLE  ALT=\"h%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k-2p ALIGN=MIDDLE  ALT=\"k-2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Bp ALIGN=MIDDLE  ALT=\"h%2Bp\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%2B2p ALIGN=MIDDLE  ALT=\"k%2B2p\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-3%2F2 ALIGN=MIDDLE  ALT=\"p=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8 ALIGN=MIDDLE  ALT=\"h=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have\r<BR>\n" );
document.write( "\n" );
document.write( " (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2B%28-3%2F2%29 ALIGN=MIDDLE  ALT=\"8%2B%28-3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3-2%28-3%2F2%29 ALIGN=MIDDLE  ALT=\"-3-2%28-3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2B%28-3%2F2%29 ALIGN=MIDDLE  ALT=\"8%2B%28-3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2B2%28-3%2F2%29 ALIGN=MIDDLE  ALT=\"-3%2B2%28-3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( " (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F2-3%2F2 ALIGN=MIDDLE  ALT=\"16%2F2-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2B3 ALIGN=MIDDLE  ALT=\"-3%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F2-3%2F2 ALIGN=MIDDLE  ALT=\"16%2F2-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3-3 ALIGN=MIDDLE  ALT=\"-3-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( " (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2 ALIGN=MIDDLE  ALT=\"13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2 ALIGN=MIDDLE  ALT=\"13%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C%0D%0Acircle%288%2C-3%2C.13%29%2Clocate%287.5%2C-2%2CV%288%2C-3%29%29%2Ccircle%2813%2F2%2C-3%2C.13%29%2Clocate%2813%2F2%2C-3%2CF%2813%2F2%2C-3%29%29%2Cline%2819%2F2%2C15%2C19%2F2%2C-15%29%2C%0D%0A+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+sqrt%28%28x-8%29%2F%28-%281%2F6%29%29%29-3%2C+-sqrt%28%28x-8%29%2F%28-%281%2F6%29%29%29-3%2C-3%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );