document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158991>Question 1158991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation for the line that goes through the two intersection points of the circle<BR>\n" );
document.write( "x2 +y2 =25andthecircle(x−8)2 +(y−4)2 =65. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782022 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=782022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Conceptually, this is a straightforward problem.  Step 1: Find the coordinates of the two points of intersection of the circles.  Step 2: Use the Two-Point Form of an equation of a straight line to create the desired equation and put it into the desired form.  However, step 1 requires some rather ugly algebra.\r<BR>\n" );
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document.write( "First we need the two circle equations expressed as functions of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ y^2\ =\ 25\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \sqrt{25\ -\ x^2}\">\r<BR>\n" );
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document.write( "And\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\,-\,8)^2\ +\ (y\,-\,4)^2\ =\ 65\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ \sqrt{65\ -\ (x\,-\,8)^2}\ +\ 4\">\r<BR>\n" );
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document.write( "By setting the two right-hand sides equal to each other, we eliminate the variable <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{25\ -\ x^2}\ =\ \sqrt{65\ -\ (x\,-\,8)^2}\ +\ 4\">\r<BR>\n" );
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document.write( "Square both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 25\ -\ x^2\ =\ 65\ -\ (x\,-\,8)^2\  +\ 8\sqrt{65\ -\ (x\,-\,8)^2}\ +\ 16\">\r<BR>\n" );
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document.write( "Simplify (I left out a lot of steps, but you can verify so that you can show your work if necessary)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -2x\ +\ 1\  =\ \sqrt{65\ -\ (x\,-\,8)^2}\">\r<BR>\n" );
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document.write( "Square both sides again:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4x^2\ -\ 4x\ +\ 1\ = 65\ -\ (x^2\ -\ 16x\ +\ 64)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5x^2\ -\ 20x\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ \in\ \{0,4\}\">\r<BR>\n" );
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document.write( "Therefore the points of intersection are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \(0,5\)\text{ and }\(4,-3\)\">\r<BR>\n" );
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document.write( "Now all that you need to do is write a function describing the set of ordered pairs that comprise the line that contains these two points.\r<BR>\n" );
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document.write( "========================================================================\r<BR>\n" );
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document.write( "I looked at my notes from this problem this morning, slapped my forehead, and got back into the system to edit my response.  No need.  Ikleyn and MathTherapy have it right.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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