document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44641>Question 44641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> plot x^2+4.y^2-4.x-8.y+4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29524 by </B><A HREF=/tutors/aboutme.mpl?userid=adamchapman><B>adamchapman(301)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=adamchapman><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=29524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4.y%5E2-4.x-8.y%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4.y%5E2-4.x-8.y%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rearrange to give a quadratic equation in terms of y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%5E2-8y%2B%28x%5E2-4x%2B4%29=0 ALIGN=MIDDLE  ALT=\"4y%5E2-8y%2B%28x%5E2-4x%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now solve the quadratic using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+ ALIGN=MIDDLE  ALT=\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "where<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=x%5E2-4x%2B4 ALIGN=MIDDLE  ALT=\"c=x%5E2-4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This should give<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%288+%2B-+sqrt%28+64-16%28x%5E2-4x%2B4%29%29%29%2F8+ ALIGN=MIDDLE  ALT=\"y+=+%288+%2B-+sqrt%28+64-16%28x%5E2-4x%2B4%29%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x%2B4 ALIGN=MIDDLE  ALT=\"x%5E2-4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > has two equal roots <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2=%28x%5E2-4x%2B4%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2=%28x%5E2-4x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the quadratic solver for y becomes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%288+%2B-+sqrt%28+64-16%28x-2%29%5E2%29%29%2F8+ ALIGN=MIDDLE  ALT=\"y+=+%288+%2B-+sqrt%28+64-16%28x-2%29%5E2%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1+%2B-+sqrt%28+64-16%28x-2%29%5E2%29%2F8+ ALIGN=MIDDLE  ALT=\"y+=+1+%2B-+sqrt%28+64-16%28x-2%29%5E2%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There are two existing solutions for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1+%2B+sqrt%28+64-16%28x-2%29%5E2%29%2F8+ ALIGN=MIDDLE  ALT=\"y+=+1+%2B+sqrt%28+64-16%28x-2%29%5E2%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1+-+sqrt%28+64-16%28x-2%29%5E2%29%2F8+ ALIGN=MIDDLE  ALT=\"y+=+1+-+sqrt%28+64-16%28x-2%29%5E2%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I have plotted both of the lines below for you.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+0%2C+4%2C+-10%2C+10%2C+1+%2B+sqrt%28+64-16%28x-2%29%5E2%29%2F8%2C+1+-+sqrt%28+64-16%28x-2%29%5E2%29%2F8%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I hope this helps.<BR>\n" );
document.write( "P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk<BR>\n" );
document.write( "Adam\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );