document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154276>Question 1154276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sketch the circle whose equation is x2 + y2 = 100. Using the same system of coordinate axes, graph the line x + 3y = 10, which should intersect the circle twice — at A = (10, 0) and at another point B in the second quadrant. Estimate the coordinates of B. Now use algebra to find them exactly. Segment AB is called a chord of the circle.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776678 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=776678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The graph of the two equations, x^2 +y^2 = 100 and x +3y = 10 is<BR>\n" );
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document.write( "Using the graph, estimate the second point to be (-8, 6)<BR>\n" );
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document.write( "solve both equations for y<BR>\n" );
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document.write( "y = sqrt(100 -x^2)<BR>\n" );
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document.write( "y = -x/3 +10/3<BR>\n" );
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document.write( "set them equal to each other<BR>\n" );
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document.write( "sqrt(100 -x^2) = -x/3 +10/3<BR>\n" );
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document.write( "square both sides<BR>\n" );
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document.write( "100 -x^2 = x^2/9 -20x/9 +100/9<BR>\n" );
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document.write( "multiply both sides of = by 9<BR>\n" );
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document.write( "900 -9x^2 = x^2 -20x +100<BR>\n" );
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document.write( "10x^2 -20x -800 = 0<BR>\n" );
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document.write( "divide both sides of = by 10<BR>\n" );
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document.write( "x^2 -2x -80 = 0<BR>\n" );
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document.write( "(x-10) * (x+8) = 0<BR>\n" );
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document.write( "therefore x = 10, x = -8<BR>\n" );
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document.write( "We know y^2 = 100 -x^2 from the first given equation<BR>\n" );
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document.write( "y^2 = 100 -(-8)^2 = 36<BR>\n" );
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document.write( "y = + or - 6<BR>\n" );
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document.write( "Since B is in the second quadrant, B = (-8, 6)<BR>\n" );
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