document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016364>Question 1016364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ellipse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2F64+%2B+y%5E2%2F25+=+1 ALIGN=MIDDLE  ALT=\"+x%5E2%2F64+%2B+y%5E2%2F25+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is given. Find the equations of the lines tangent to this ellipse which make an angle of 60 degrees with the x-axis.\r<BR>\n" );
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document.write( "can someone show me how to do and answer it. thank you very much for help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #632760 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=632760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The ellipse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2F64+%2B+y%5E2%2F25+=+1 ALIGN=MIDDLE  ALT=\"+x%5E2%2F64+%2B+y%5E2%2F25+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is given. Find the equations of the lines tangent to this ellipse which make an angle of 60 degrees with the x-axis.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2F64+%2B+y%5E2%2F25+=+1 ALIGN=MIDDLE  ALT=\"+x%5E2%2F64+%2B+y%5E2%2F25+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the slope of the ellipse at any point.<BR>\n" );
document.write( "Slope m = dy/dx<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2%2F64+%2B+y%5E2%2F25+=+1 ALIGN=MIDDLE  ALT=\"+x%5E2%2F64+%2B+y%5E2%2F25+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Differentiate implicitly<BR>\n" );
document.write( "(x/32) dx + (2y/25)dy = 0<BR>\n" );
document.write( "dy/dx = -25x/(64y)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The slope of 60 degs with the x-axis is tan(60) = sqrt(3)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25x%2F%2864y%29+=+sqrt%283%29 ALIGN=MIDDLE  ALT=\"-25x%2F%2864y%29+=+sqrt%283%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+=+-+64%2Asqrt%283%29y%2F25 ALIGN=MIDDLE  ALT=\"x+=+-+64%2Asqrt%283%29y%2F25\"   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%2F64+%2B+y%5E2%2F25+=+1 ALIGN=MIDDLE  ALT=\"+x%5E2%2F64+%2B+y%5E2%2F25+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2+%2B+64y%5E2+=+1600 ALIGN=MIDDLE  ALT=\"25x%5E2+%2B+64y%5E2+=+1600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sub for x in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2+%2B+64y%5E2+=+1600 ALIGN=MIDDLE  ALT=\"25x%5E2+%2B+64y%5E2+=+1600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4096%2A3y%5E2%2F25+%2B+64y%5E2+=+1600 ALIGN=MIDDLE  ALT=\"4096%2A3y%5E2%2F25+%2B+64y%5E2+=+1600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12288y%5E2+%2B+1600y%5E2+=+40000%7D%7D%0D%0A%7B%7B%7B13888y%5E2+=+40000 ALIGN=MIDDLE  ALT=\"12288y%5E2+%2B+1600y%5E2+=+40000%7D%7D%0D%0A%7B%7B%7B13888y%5E2+=+40000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=217y%5E2+=+625 ALIGN=MIDDLE  ALT=\"217y%5E2+=+625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+625%2F217 ALIGN=MIDDLE  ALT=\"y%5E2+=+625%2F217\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sub for y^2 in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2+%2B+64y%5E2+=+1600 ALIGN=MIDDLE  ALT=\"25x%5E2+%2B+64y%5E2+=+1600\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find x^2<BR>\n" );
document.write( "x^2 = 12288/217 = 4096*3/217<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B64%2Asqrt%283%2F217%29 ALIGN=MIDDLE  ALT=\"x+=+%2B64%2Asqrt%283%2F217%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+=+-64%2Asqrt%283%2F217%29 ALIGN=MIDDLE  ALT=\"x+=+-64%2Asqrt%283%2F217%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2+%2B+64y%5E2+=+1600 ALIGN=MIDDLE  ALT=\"25x%5E2+%2B+64y%5E2+=+1600\"   DISABLED_style= \"max-width:90%; height:auto;\" > for y^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+625%2F217 ALIGN=MIDDLE  ALT=\"y%5E2+=+625%2F217\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2B25%2Fsqrt%28217%29 ALIGN=MIDDLE  ALT=\"y+=+%2B25%2Fsqrt%28217%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-25%2Fsqrt%28217%29 ALIGN=MIDDLE  ALT=\"y+=+-25%2Fsqrt%28217%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "For +60 degs with the x-axis, when x is +, y is negative, and vice versa.<BR>\n" );
document.write( "The tangent points are:<BR>\n" );
document.write( "(+64*sqrt(3/217),-25/sqrt(217))<BR>\n" );
document.write( "--> y + (25/sqrt(217)) = sqrt(3)*(x - 64*sqrt(3/217))<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(-64*sqrt(3/217),+25/sqrt(217))<BR>\n" );
document.write( "--> y - (25/sqrt(217)) = sqrt(3)*(x + 64*sqrt(3/217))<BR>\n" );
document.write( " </SPAN>\n" );
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