document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039233>Question 1039233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle which touches the X axis at the point (3,0) and cuts off an intercept 8 units from the positive part of the y axis </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #653976 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20054)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=653976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle which touches the X axis at the point (3,0) and cuts off an intercept 8 units from the positive part of the y axis\r<BR>\n" );
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document.write( "The standard equation of any circle is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since it is tangent to the x-axis at (3,0),<BR>\n" );
document.write( "the center is directly above (3,0), so its<BR>\n" );
document.write( "center also has x-coordinate 3. So h=3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It passes through (x,y) = (3,0), so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-3%29%5E2%2B%280-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%283-3%29%5E2%2B%280-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=0%5E2%2Bk%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"0%5E2%2Bk%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=k%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"k%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "k and r are both positive numbers.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=r ALIGN=MIDDLE  ALT=\"k=r\"   DISABLED_style= \"max-width:90%; height:auto;\" > and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%5E2%2B%28y-r%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B%28y-r%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It has a y-intercept at (0,8)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280-3%29%5E2%2B%288-r%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%280-3%29%5E2%2B%288-r%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=%28-3%29%5E2%2B64-16r%2Br%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28-3%29%5E2%2B64-16r%2Br%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=9%2B64-16r%2Br%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"9%2B64-16r%2Br%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=73-16r=0 ALIGN=MIDDLE  ALT=\"73-16r=0\"   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=-16r=-73 ALIGN=MIDDLE  ALT=\"-16r=-73\"   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=r=%28-73%29%2F%28-16%29 ALIGN=MIDDLE  ALT=\"r=%28-73%29%2F%28-16%29\"   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=r=73%2F16 ALIGN=MIDDLE  ALT=\"r=73%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=r=73%2F16 ALIGN=MIDDLE  ALT=\"x=r=73%2F16\"   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=%28x-3%29%5E2%2B%28y-73%2F16%29%5E2=%2873%2F16%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E2%2B%28y-73%2F16%29%5E2=%2873%2F16%29%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=drawing%284800%2F13%2C400%2C-3%2C9%2C+-3%2C10%2Ccircle%283%2C+73%2F16%2C.1%29%2C%0D%0Alocate%283%2C73%2F16%2C%28matrix%281%2C3%2C3%2C%22%2C%22%2C73%2F16%29%29%29%2C%0D%0A%0D%0Agraph%284800%2F13%2C400%2C-3%2C9%2C+-3%2C10%29%2C+circle%283%2C73%2F16%2C73%2F16%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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