document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150361>Question 150361</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me find the focus and the dirctrix of the parabola 16x^2=y.<BR>\n" );
document.write( "There are 4 choices for an answer:<BR>\n" );
document.write( "1. Focus (0,4), directrix y=-4<BR>\n" );
document.write( "2. Focus (0,1/4), directrix y=-1/4<BR>\n" );
document.write( "3. Focus (0,1/16), directrix y=-1/16<BR>\n" );
document.write( "4. Focus (0,1/64), directrix y=-1/64<BR>\n" );
document.write( "Thank you for your time and help, Natalie! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110465 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 16x^2=y.<BR>\n" );
document.write( "There are 4 choices for an answer:<BR>\n" );
document.write( "1. Focus (0,4), directrix y=-4<BR>\n" );
document.write( "2. Focus (0,1/4), directrix y=-1/4<BR>\n" );
document.write( "3. Focus (0,1/16), directrix y=-1/16<BR>\n" );
document.write( "4. Focus (0,1/64), directrix y=-1/64<BR>\n" );
document.write( "Thank you for your time and help, Natalie!<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The standard from for parabolas is x^2=4py<BR>\n" );
document.write( "So y = x^2/4p = 16x^2<BR>\n" );
document.write( "x^2/4p = 16x^2<BR>\n" );
document.write( "4p = x^2/16x^2 = 1/16<BR>\n" );
document.write( "p = 1/64<BR>\n" );
document.write( "P is the distance from the Origin to the directrix, and (0,p) is the focus.<BR>\n" );
document.write( "That's answer #4.<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2%2B0x%2B0+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2%2B0x%2B0+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%280%29%5E2-4%2A16%2A0=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%280%29%5E2-4%2A16%2A0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=0 is zero! That means that there is only one solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%280%29%29%2F2%5C16 ALIGN=MIDDLE  ALT=\"x+=+%28-%280%29%29%2F2%5C16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "      Expression can be factored: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2%2B0x%2B0+=+%28x-0%29%2A%28x-0%29 ALIGN=MIDDLE  ALT=\"16x%5E2%2B0x%2B0+=+%28x-0%29%2A%28x-0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Again, the answer is: 0, 0.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B0%2Ax%2B0+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B0%2Ax%2B0+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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