document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209461>Question 1209461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The line y= mx + c is tangent to the curve x^2 + y^2 = 4. Prove that 4m^2 = c^2 - 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848886 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848886\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The graph of x^2+y^2=4 is a circle with center at the origin and radius 2.<br><BR>\n" );
document.write( "Let O be the origin; let A and B be the y- and x-intercepts of the line y=mx+c; and let C be the point of tangency with the circle.<br><BR>\n" );
document.write( "AOB is a right triangle, and OC is the altitude to the hypotenuse.<br><BR>\n" );
document.write( "The y- and x-intercepts of the given line are<br><BR>\n" );
document.write( "A(0,c)<BR>\n" );
document.write( "B(c/m,0)<br><BR>\n" );
document.write( "That gives us the lengths of the legs of triangle AOB as<br><BR>\n" );
document.write( "OA = c<BR>\n" );
document.write( "OB = c/m<br><BR>\n" );
document.write( "In right triangle ACO, OA = c and OC = 2, so AC = sqrt(c^2-4).<br><BR>\n" );
document.write( "Triangles AOB and ACO are similar.  Set up and solve a proportion using the lengths of the legs of those two triangles.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fsqrt%28c%5E2-4%29=%28c%2Fm%29%2Fc ALIGN=MIDDLE  ALT=\"2%2Fsqrt%28c%5E2-4%29=%28c%2Fm%29%2Fc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fsqrt%28c%5E2-4%29=1%2Fm ALIGN=MIDDLE  ALT=\"2%2Fsqrt%28c%5E2-4%29=1%2Fm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28c%5E2-4%29=1%2Fm%5E2 ALIGN=MIDDLE  ALT=\"4%2F%28c%5E2-4%29=1%2Fm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2-4=m%5E2 ALIGN=MIDDLE  ALT=\"c%5E2-4=m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "QED....<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );