document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=437159>Question 437159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many lines with a slope of -1 are tangent to the circle x^2 + y^2 = 25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302406 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=302406\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How many lines with a slope of -1 are tangent to the circle x^2 + y^2 = 25<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x^2 + y^2 = 25<BR>\n" );
document.write( "There would be two points where a line of -1 slope would be tangent to the circle. The (x,y) coordinates at the two points would be (5sqrt(2)/2,5sqrt(2)/2) and (-5sqrt(2)/2,-5sqrt(2)/2)<BR>\n" );
document.write( "Using the standard form for a straight line, y=mx+b, we have (x,y) coordinates of a point on each line. All we need is find b to complete the equation.<BR>\n" );
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document.write( "For the first line:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "5sqrt(2)/2=(-1)5sqrt(2)/2+b<BR>\n" );
document.write( "5sqrt(2)=b<BR>\n" );
document.write( "Equation of line: y=-x+5sqrt(2)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "For the second line:<BR>\n" );
document.write( "y=mx+b<BR>\n" );
document.write( "-5sqrt(2)/2=(-1)-5sqrt(2)/2+b<BR>\n" );
document.write( "-5sqrt(2)=b<BR>\n" );
document.write( "Equation of line: y=-x-5sqrt(2)<BR>\n" );
document.write( "see graph below:<BR>\n" );
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document.write( "y=+-(25-x^2)^.5<BR>\n" );
document.write( "y=-x+5*2^.5<BR>\n" );
document.write( "y=-x-5*2^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+%2825-x%5E2%29%5E.5%2C-%2825-x%5E2%29%5E.5%2C-x%2B5%2A2%5E.5%2C-x-5%2A2%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );