document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=771657>Question 771657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need your help<BR>\n" );
document.write( " The equation of a circle with radius is (x-h)^2+ (y-k)^2 if the center is at (h,k) Find the condition that a circle shall<BR>\n" );
document.write( "a. touch the x-axis<BR>\n" );
document.write( "b.have its center on the y-axis<BR>\n" );
document.write( "c.touch both axes<BR>\n" );
document.write( "d.have its center on the line 3x+4y=12<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470372 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=470372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of a circle with radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <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;\" > if the center is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28h%2Ck%29%22 ALIGN=MIDDLE  ALT=\"%22%28h%2Ck%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Each of the conditions sets (fixes) something about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but one or two of those variables will still be free to take any value. The un-fixed variable(s) will still be in the equation, and the equation will represent an infinite number of circles.<BR>\n" );
document.write( " <BR>\n" );
document.write( "a. If the circle touches the x-axis (is tangent to the x-axis), the center is at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the x-axis, at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28h%2Cr%29%22 ALIGN=MIDDLE  ALT=\"%22%28h%2Cr%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-0.1%2C0.9%2C-0.1%2C0.9%2C%0D%0Agrid%280%29%2C+circle%280.4%2C0.35%2C0.35%29%2C%0D%0Agreen%28line%280.4%2C0%2C0.4%2C0.35%29%29%2Clocate%280.41%2C0.2%2Cgreen%28r%29%29%2C%0D%0Ablue%28circle%280.4%2C0.35%2C0.01%29%29%2Clocate%280.4%2C0.35%2Cblue%28%22%28h%2Cr%29%22%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > so the equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-h%29%5E2%2B+%28y-r%29%5E2=r%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-h%29%5E2%2B+%28y-r%29%5E2=r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "b. If the circle has its center on the y-axis (which is the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the center is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%280%2Ck%29%22 ALIGN=MIDDLE  ALT=\"%22%280%2Ck%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%2B+%28y-k%29%5E2=r%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2B+%28y-k%29%5E2=r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "c. If the circle touches both axes, the center is at a distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both axes, at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%28r%2Cr%29%22 ALIGN=MIDDLE  ALT=\"%22%28r%2Cr%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-r%29%5E2%2B+%28y-r%29%5E2=r%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-r%29%5E2%2B+%28y-r%29%5E2=r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "d. If the circle has its center on the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B4y=12 ALIGN=MIDDLE  ALT=\"3x%2B4y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28200%2C200%2C-1%2C5%2C-1%2C5%2C%0D%0Agrid%280%29%2Cline%28-4%2C6%2C8%2C-3%29%29 ALIGN=MIDDLE  ALT=\"drawing%28200%2C200%2C-1%2C5%2C-1%2C5%2C%0D%0Agrid%280%29%2Cline%28-4%2C6%2C8%2C-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3h%2B4k=12 ALIGN=MIDDLE  ALT=\"3h%2B4k=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4k=12-3h ALIGN=MIDDLE  ALT=\"4k=12-3h\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%2812-3h%29%2F4 ALIGN=MIDDLE  ALT=\"k=%2812-3h%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3-%283%2F4%29h ALIGN=MIDDLE  ALT=\"k=3-%283%2F4%29h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the equation gets ugly:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-h%29%5E2%2B+%28y-4%2B%283%2F4%29h%29%5E2=r%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-h%29%5E2%2B+%28y-4%2B%283%2F4%29h%29%5E2=r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );