document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030424>Question 1030424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x - 2y = 10.\r<BR>\n" );
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document.write( "Give your answer as a list of points separated by semicolons, with the points ordered such that their x-coordinates are in increasing order. (So \"(1,-3); (2,3); (5,-7)\" - without the quotes - is a valid answer format.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645287 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=645287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x - 2y = 10. <BR>\n" );
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document.write( "13 units away is a circle ::<BR>\n" );
document.write( "(x-2)^2 + (y-7)^2 = 13^2<BR>\n" );
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document.write( "lie on the line::<BR>\n" );
document.write( "x = 2y+10<BR>\n" );
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document.write( "Substitute into the circle equation:<BR>\n" );
document.write( "(2y+10-2)^2 + (y-7)^2 = 169<BR>\n" );
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document.write( "(2y+8)^2 + (y-7)^2  = 169<BR>\n" );
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document.write( "4y^2 + 32y + 64 + y^2 - 14y + 49 = 169<BR>\n" );
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document.write( "5y^2 + 18y -56 = 0<BR>\n" );
document.write( "(y-2)(5y+28) = 0<BR>\n" );
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document.write( "y = 3 or y = -28/5<BR>\n" );
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document.write( "x = 2*3+10 = 16 or x = 2(-28/5)+10 = (-56/5)+ 10 = -6/5<BR>\n" );
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document.write( "Points:: (16,3) ; (-6/5,-28/5)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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