document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199583>Question 1199583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle has its center at (0,0) and its radius is 10 units. Determine the equations of the lines through (15,15) and tangent to the circle.<BR>\n" );
document.write( "A. x-2.897y+34.450=0 and x-0.303y-10.450=0<BR>\n" );
document.write( "B. x-3.297y+34.450=0 and x-0.303y-10.450=0<BR>\n" );
document.write( "C. x-2.897y+34.450=0 and x-0.353y-10.450=0<BR>\n" );
document.write( "D. x-23.297y+34.450=0 and x-0.353y-10.450=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833590 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=833590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "ANSWER: B<br><BR>\n" );
document.write( "You won't learn anything from this if we solve the problem for you, so I will outline how you can get the answer and let you do the work.<br><BR>\n" );
document.write( "Let (x,y) be a point on the circle.<br><BR>\n" );
document.write( "The slope of the line from (15,15) to (x,y) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815-y%29%2F%2815-x%29 ALIGN=MIDDLE  ALT=\"%2815-y%29%2F%2815-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The slope of the radius of the circle from the center (0,0) to (x,y) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Fx ALIGN=MIDDLE  ALT=\"y%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "A tangent and a radius to the point of tangency are perpendicular, so the product of their slopes is -1:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815-y%29%2F%2815-x%29%28y%2Fx%29=-1 ALIGN=MIDDLE  ALT=\"%2815-y%29%2F%2815-x%29%28y%2Fx%29=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "Work with that equation until you get to the point where the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=A ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=A\"   DISABLED_style= \"max-width:90%; height:auto;\" > where A is an expression in x and y.<br><BR>\n" );
document.write( "We also know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=100 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > [2]<br><BR>\n" );
document.write( "so<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=100 ALIGN=MIDDLE  ALT=\"A=100\"   DISABLED_style= \"max-width:90%; height:auto;\" > [3]<br><BR>\n" );
document.write( "Solve equation [3] for y in terms of x and substitute in [2] to get an equation in x alone.<br><BR>\n" );
document.write( "Use a graphing calculator or similar tool to find the coordinates of the point of tangency.<br><BR>\n" );
document.write( "Note that, by the symmetry of the problem, if one of the points of tangency is (a,-b), then the other point of tangency is (-b,a).<br><BR>\n" );
document.write( "Use the two points of tangency and the fixed point (15,15) to find that the equations of the tangents are as given in answer choice B.<br><BR>\n" );
document.write( " </SPAN>\n" );
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