document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=678416>Question 678416</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle if it is tangent to the line x+y=2 at point (4,-2) and the center at x-axis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #421400 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=421400\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+h%29%5E+2+%2B+%28y+-+k%29+%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+h%29%5E+2+%2B+%28y+-+k%29+%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(h,k)-center and r radius\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( "given:\r<BR>\n" );
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document.write( " the circle if it is tangent to the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=2 ALIGN=MIDDLE  ALT=\"x%2By=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > at point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and the center at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-axis ALIGN=MIDDLE  ALT=\"x-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find the equation of the circle:\r<BR>\n" );
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document.write( "Let ... C(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) be the center.\r<BR>\n" );
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document.write( "Also, let the line L :<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=2 ALIGN=MIDDLE  ALT=\"x%2By=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > touch\r<BR>\n" );
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document.write( "this circle at the point A(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+2 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%281%29x+%2B2 ALIGN=MIDDLE  ALT=\"y+=+-%281%29x+%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B1%5D+=+-1 ALIGN=MIDDLE  ALT=\"m%5B1%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and slope of seg AC is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5B2%5D+=+%28+-2-0+%29+%2F+%28+4+-a+%29+=+-2+%2F+%28+4-a+%29 ALIGN=MIDDLE  ALT=\"m%5B2%5D+=+%28+-2-0+%29+%2F+%28+4+-a+%29+=+-2+%2F+%28+4-a+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Since line L is perpendicular to segment AC, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m%5B1%5D%2Am%5B2+%5D=+1 ALIGN=MIDDLE  ALT=\"+m%5B1%5D%2Am%5B2+%5D=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29+%2A+%28-2+%2F+%28+4+-a+%29+%29+=+1 ALIGN=MIDDLE  ALT=\"%28-1%29+%2A+%28-2+%2F+%28+4+-a+%29+%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F+%28+4+-a+%29+=+1 ALIGN=MIDDLE  ALT=\"-2%2F+%28+4+-a+%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=++4-a+ ALIGN=MIDDLE  ALT=\"-2=++4-a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+4%2B2 ALIGN=MIDDLE  ALT=\"a+=+4%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+6 ALIGN=MIDDLE  ALT=\"a+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hence, C &#8801; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) &#8801; (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\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/plot-formula.mpl?expression=r%5E2+=+%28AC%29%5E2+=+%286-4%29%5E2+%2B+%280%2B2%29%5E2+=%282%29%5E2+%2B+%282%29%5E2+=+8 ALIGN=MIDDLE  ALT=\"r%5E2+=+%28AC%29%5E2+=+%286-4%29%5E2+%2B+%280%2B2%29%5E2+=%282%29%5E2+%2B+%282%29%5E2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hence, by Center-Radius Form, eq of circle is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+x+-+h+%29%5E2+%2B+%28+y+-+k+%29%5E2++=+r%5E2+ ALIGN=MIDDLE  ALT=\"%28+x+-+h+%29%5E2+%2B+%28+y+-+k+%29%5E2++=+r%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+x+-+2+%29%5E2++%2B+%28+y+-+0+%29%5E2++=+8+ ALIGN=MIDDLE  ALT=\"%28+x+-+2+%29%5E2++%2B+%28+y+-+0+%29%5E2++=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+x+-+2+%29%5E2++%2B+y+%5E2++=+8 ALIGN=MIDDLE  ALT=\"%28+x+-+2+%29%5E2++%2B+y+%5E2++=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >......... your answer\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-10%2C10%2C-10%2C10%2Cgrid%281%29%2Ccircle%286%2C0%2C2.83%29%2Ccircle%284%2C-2%2C0.2%29%2Cgraph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-x%2B2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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