document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=916230>Question 916230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation x^2+y^2=169 defines a circle with its center at the origin and a radius of 13. The line y=x-7 passes through the circle. Determine the circle and line line intersect.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555972 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=555972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we are given circle x^2+y^2=169 and line y = x-7<BR>\n" );
document.write( "substitute for y in the circle equation using line value for y<BR>\n" );
document.write( "x^2 +(x-7)^2 = 169<BR>\n" );
document.write( "x^2 + x^2 -14x +49 = 169<BR>\n" );
document.write( "2x^2 -14x -120 = 0<BR>\n" );
document.write( "divide both sides of = by 2<BR>\n" );
document.write( "x^2 -7x -60 = 0<BR>\n" );
document.write( "factor polynomial<BR>\n" );
document.write( "(x+5)*(x-12) = 0<BR>\n" );
document.write( "x = -5 and 12<BR>\n" );
document.write( "therefore the two points of intersection are<BR>\n" );
document.write( "(-5, -12) and (12, 5)<BR>\n" );
document.write( "to find the y value for the points just use the equation for the line<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );