document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=990255>Question 990255</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle passes through the Point (8,7) and touches the y-axis at the Point (0,3). Find the equation of the circle. if the circle cuts the x-axis at D and E, find the equation of another circle which is DE as diameter. \r<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 #610295 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39626)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=610295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Unknown center of the first circle, (h,k).<BR>\n" );
document.write( "Using Distance Formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28h-8%29%5E2%2B%28k-7%29%5E2=%28h-0%29%5E2%2B%28k-3%29%5E2 ALIGN=MIDDLE  ALT=\"%28h-8%29%5E2%2B%28k-7%29%5E2=%28h-0%29%5E2%2B%28k-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28h-8%29%5E2%2B%28k-7%29%5E2=h%5E2%2B%28k-3%29%5E2 ALIGN=MIDDLE  ALT=\"%28h-8%29%5E2%2B%28k-7%29%5E2=h%5E2%2B%28k-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2-16h%2B64%2Bk%5E2-14k%2B49=h%5E2%2Bk%5E2-6k%2B9 ALIGN=MIDDLE  ALT=\"h%5E2-16h%2B64%2Bk%5E2-14k%2B49=h%5E2%2Bk%5E2-6k%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16h%2B64-14k%2B49=-6k%2B9 ALIGN=MIDDLE  ALT=\"-16h%2B64-14k%2B49=-6k%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16h-14k%2B6k%2B64%2B49-9=0 ALIGN=MIDDLE  ALT=\"-16h-14k%2B6k%2B64%2B49-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16h-8k%2B64%2B40=0 ALIGN=MIDDLE  ALT=\"-16h-8k%2B64%2B40=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16h%2B8k=104 ALIGN=MIDDLE  ALT=\"16h%2B8k=104\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h%2Bk=13 ALIGN=MIDDLE  ALT=\"2h%2Bk=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This circle touching, just touching, the y-axis at (0,3) means that the center is some point on the line y=3.  This means, you can solve for h, because you know  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-3 ALIGN=MIDDLE  ALT=\"k=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is based on knowing how the standard circle equation works.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h=13-k ALIGN=MIDDLE  ALT=\"2h=13-k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h=13-%28-3%29 ALIGN=MIDDLE  ALT=\"2h=13-%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2h=16 ALIGN=MIDDLE  ALT=\"2h=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8 ALIGN=MIDDLE  ALT=\"h=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Center of this first circle is therefore,  (8,-3).  The point (0,3) on the circle may be the convenient point to again use the Distance Formula, to find the radius of this circle.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=%288-0%29%5E2%2B%28-3-0%29%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=%288-0%29%5E2%2B%28-3-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=8%5E2 ALIGN=MIDDLE  ALT=\"r%5E2=8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=8 ALIGN=MIDDLE  ALT=\"r=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This first circle equation is then,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-8%29%5E2%2B%28y%2B3%29=8%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-8%29%5E2%2B%28y%2B3%29=8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I have not finished to do the final question, but maybe you can. </SPAN>\n" );
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