document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012679>Question 1012679</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the circle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-6x-8y%2B9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-6x-8y%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a secant line y=x. Determine the length of the corresponding secant segment. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628682 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=628682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have two equations that need to be solved simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the solution will be common to both equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equations are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^2 + y^2 - 6x - 8y + 9 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace y with x in the first equataion to get x^2 + x^2 - 6x - 8x + 9 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get 2x^2 - 14x + 9 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve this quadratic equation to get x = .71612 or x = 6.28388 rounded to 5 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since y = x, the coordinate points are (.71612,.71612) or (6.28388,6.28388).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "these points are the points of intersection between the circle and the secant line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for the length of that secant line is L = sqrt((x2-x1)^2 + (y2-y1)^2).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that becomes L = sqrt((6.28388-.71612)^2 + (6.28388-.71612)^2).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this results in L = 7.874 rounded to 3 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can also find the intersection points by graphing as shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/010701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );