document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=824702>Question 824702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> plz help me to find out the points of intersection of parabolas y^2=4x and x^2=64y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #496714 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=496714\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Substitution Method: <BR>\n" );
document.write( "1. Solve one equation for one of the variables.<BR>\n" );
document.write( "Solving the first equation for x (by dividing each side by 4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2F4+=+x ALIGN=MIDDLE  ALT=\"y%5E2%2F4+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2. Substitute for the solved-for variable in the other equation:<BR>\n" );
document.write( "(y^2/4)^2 = 64y<BR>\n" );
document.write( "3. Solve the one-variable equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4%2F16+=+64y ALIGN=MIDDLE  ALT=\"y%5E4%2F16+=+64y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by 16 to eliminate the fraction:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4+=+1024y ALIGN=MIDDLE  ALT=\"y%5E4+=+1024y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 1024y (to get a zero on one side):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4+-+1024y=+0 ALIGN=MIDDLE  ALT=\"y%5E4+-+1024y=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor out the GCF of y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%28y%5E3+-+1024%29=+0 ALIGN=MIDDLE  ALT=\"y%28y%5E3+-+1024%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Zero Product Property:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3-1024+=+0 ALIGN=MIDDLE  ALT=\"y%5E3-1024+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving the second equation...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3=1024 ALIGN=MIDDLE  ALT=\"y%5E3=1024\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=root%283%2C+1024%29+=+root%283%2C+512%2A2%29+=+root%283%2C+512%29%2Aroot%283%2C+2%29+=+8root%283%2C+2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4. Use the solution(s) to the one-variable equation to find the solution(s) for the other variable:<BR>\n" );
document.write( "For y = 0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29%5E2+=+4x ALIGN=MIDDLE  ALT=\"%280%29%5E2+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so x = 0, making (0, 0) a point of intersection.<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+8root%283%2C+2%29 ALIGN=MIDDLE  ALT=\"y+=+8root%283%2C+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288root%283%2C+2%29%29%5E2+=+4x ALIGN=MIDDLE  ALT=\"%288root%283%2C+2%29%29%5E2+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64root%283%2C+4%29+=+4x ALIGN=MIDDLE  ALT=\"64root%283%2C+4%29+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16root%283%2C+4%29+=+x ALIGN=MIDDLE  ALT=\"16root%283%2C+4%29+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "making (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16root%283%2C+4%29 ALIGN=MIDDLE  ALT=\"16root%283%2C+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8root%283%2C+2%29 ALIGN=MIDDLE  ALT=\"8root%283%2C+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) a second point of intersection. Here's a graph to illustrate:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C+600%2C+-10%2C+30%2C+-10%2C+30%2C+sqrt%284x%29%2C+-sqrt%284x%29%2C+x%5E2%2F64%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Don't mind the colors.) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );