document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156565>Question 1156565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem is stated thus: A circle is tangent to the y-axis at y=3 and has one x-intercept at x=1. <BR>\n" );
document.write( "a. Determine the other x-intercept<BR>\n" );
document.write( "b. deduce the equation of the circle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779291 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=779291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first thing I would do is draw a diagram and label some points.\r<BR>\n" );
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document.write( "Since the distance from the center of the circle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   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=%28r+-1%29%5E2%2B+%283+-0%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28r+-1%29%5E2%2B+%283+-0%29%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   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%5E2-2r%2B1+%2B+9+=+r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2-2r%2B1+%2B+9+=+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=r%5E2-r%5E2+-+2r%2B1+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"r%5E2-r%5E2+-+2r%2B1+%2B+9+=+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=-2r%2B10+=+0 ALIGN=MIDDLE  ALT=\"-2r%2B10+=+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=+10+=2r ALIGN=MIDDLE  ALT=\"+10+=2r\"   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=5 ALIGN=MIDDLE  ALT=\"r=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "yor equation 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+=+5%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+h%29%5E2+%2B+%28y-k%29%5E2+=+5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........use given point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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;\" >) to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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=%281+-+h%29%5E2+%2B+%280-k%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%281+-+h%29%5E2+%2B+%280-k%29%5E2+=+25\"   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=1+-+2h%2Bh%5E2+%2B+k%5E2+=+25 ALIGN=MIDDLE  ALT=\"1+-+2h%2Bh%5E2+%2B+k%5E2+=+25\"   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=+-+2h%2Bh%5E2+%2B+k%5E2+=+24 ALIGN=MIDDLE  ALT=\"+-+2h%2Bh%5E2+%2B+k%5E2+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.1\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+=+5%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+h%29%5E2+%2B+%28y-k%29%5E2+=+5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........use given point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=%280+-+h%29%5E2+%2B+%283-k%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%280+-+h%29%5E2+%2B+%283-k%29%5E2+=+25\"   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=h%5E2+%2B+k%5E2-6k+%2B9=+25 ALIGN=MIDDLE  ALT=\"h%5E2+%2B+k%5E2-6k+%2B9=+25\"   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=h%5E2+%2B+k%5E2-6k+=+16 ALIGN=MIDDLE  ALT=\"h%5E2+%2B+k%5E2-6k+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............eq.2\r<BR>\n" );
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document.write( "solve the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+2h%2Bh%5E2+%2B+k%5E2+=+24 ALIGN=MIDDLE  ALT=\"+-+2h%2Bh%5E2+%2B+k%5E2+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+%2B+k%5E2-6k+=+16 ALIGN=MIDDLE  ALT=\"h%5E2+%2B+k%5E2-6k+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............eq.2<BR>\n" );
document.write( "---------------------------------------------------------subtract\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+2h%2Bh%5E2+%2B+k%5E2-%28h%5E2+%2B+k%5E2-6k%29+=+24-16 ALIGN=MIDDLE  ALT=\"+-+2h%2Bh%5E2+%2B+k%5E2-%28h%5E2+%2B+k%5E2-6k%29+=+24-16\"   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=+-+2h%2Bh%5E2+%2B+k%5E2-h%5E2+-+k%5E2%2B6k+=+8 ALIGN=MIDDLE  ALT=\"+-+2h%2Bh%5E2+%2B+k%5E2-h%5E2+-+k%5E2%2B6k+=+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=+-+2h+%2B6k+=+8 ALIGN=MIDDLE  ALT=\"+-+2h+%2B6k+=+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=+-+h+%2B3k+=+4 ALIGN=MIDDLE  ALT=\"+-+h+%2B3k+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   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=+-+4%2B3k+=+h ALIGN=MIDDLE  ALT=\"+-+4%2B3k+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........eq.1a\r<BR>\n" );
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document.write( "go to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+%2B+k%5E2-6k+=+16 ALIGN=MIDDLE  ALT=\"h%5E2+%2B+k%5E2-6k+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............eq.2, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   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-+4%2B3k%29%5E2+%2B+k%5E2-6k+=+16 ALIGN=MIDDLE  ALT=\"%28-+4%2B3k%29%5E2+%2B+k%5E2-6k+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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=10+k%5E2+-+30+k+%2B+16+=+16 ALIGN=MIDDLE  ALT=\"10+k%5E2+-+30+k+%2B+16+=+16\"   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=10+k%5E2+-+30k++=+16-16 ALIGN=MIDDLE  ALT=\"10+k%5E2+-+30k++=+16-16\"   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=10+k%5E2+-+30k++=+0 ALIGN=MIDDLE  ALT=\"10+k%5E2+-+30k++=+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=+k%5E2+-+3k++=+0 ALIGN=MIDDLE  ALT=\"+k%5E2+-+3k++=+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=k%28+k+-+3%29++=+0 ALIGN=MIDDLE  ALT=\"k%28+k+-+3%29++=+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=k+=+0 ALIGN=MIDDLE  ALT=\"k+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<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;\" >\r<BR>\n" );
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document.write( "\n" );
document.write( "go to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-+4%2B3k+=+h ALIGN=MIDDLE  ALT=\"+-+4%2B3k+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........eq.1a, substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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=+-+4%2B3%2A0+=+h ALIGN=MIDDLE  ALT=\"+-+4%2B3%2A0+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4 ALIGN=MIDDLE  ALT=\"h=-4\"   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=+-+4%2B3%2A3+=+h ALIGN=MIDDLE  ALT=\"+-+4%2B3%2A3+=+h\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=5 ALIGN=MIDDLE  ALT=\"h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions for coordinates of the center<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-4 ALIGN=MIDDLE  ALT=\"h+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+0 ALIGN=MIDDLE  ALT=\"k+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> disregard, because point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is a point where circle touches y-axis\r<BR>\n" );
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document.write( "your coordinates of the center:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+5 ALIGN=MIDDLE  ALT=\"h+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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;\" >\r<BR>\n" );
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document.write( "and your equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+5%29%5E2+%2B+%28y-3%29%5E2+=+25 ALIGN=MIDDLE  ALT=\"%28x+-+5%29%5E2+%2B+%28y-3%29%5E2+=+25\"   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=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Csqrt%28-%28x+-+5%29%5E2+%2B25%29+%2B3%2C-sqrt%28-%28x+-+5%29%5E2+%2B25%29%2B3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );