document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204503>Question 204503</A>: <I><SPAN STYLE=\"word-break: break-all;\">  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154379 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=154379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29=%28x%2Bh%29%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29=%28x%2Bh%29%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace each \"x\" with \"x+h\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29=x%5E2%2B2xh%2Bh%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29=x%5E2%2B2xh%2Bh%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL (ie expand)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the given difference quotient.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B2xh%2Bh%5E2%2B3-%28x%5E2%2B3%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2xh%2Bh%5E2%2B3-%28x%5E2%2B3%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%2Bh%29=x%5E2%2B2xh%2Bh%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%2Bh%29=x%5E2%2B2xh%2Bh%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B3\"   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%5E2%2B2xh%2Bh%5E2%2B3-x%5E2-3%29%2Fh ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2xh%2Bh%5E2%2B3-x%5E2-3%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282xh%2Bh%5E2%29%2Fh ALIGN=MIDDLE  ALT=\"%282xh%2Bh%5E2%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28h%282x%2Bh%29%29%2Fh ALIGN=MIDDLE  ALT=\"%28h%282x%2Bh%29%29%2Fh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF \"h\" from the numerator.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28h%29%282x%2Bh%29%29%2Fcross%28h%29 ALIGN=MIDDLE  ALT=\"%28cross%28h%29%282x%2Bh%29%29%2Fcross%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Bh ALIGN=MIDDLE  ALT=\"2x%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%2Bh%29-f%28x%29%29%2Fh=2x%2Bh ALIGN=MIDDLE  ALT=\"%28f%28x%2Bh%29-f%28x%29%29%2Fh=2x%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E2%2B3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E2%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "Take note that when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > it is less than zero. Because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x ALIGN=MIDDLE  ALT=\"f%28x%29=-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C0 ALIGN=MIDDLE  ALT=\"x%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that we simply plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=-%28-3%29=3 ALIGN=MIDDLE  ALT=\"f%28-3%29=-%28-3%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29=3 ALIGN=MIDDLE  ALT=\"f%28-3%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > it is greater than zero. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we just plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=%282%29%5E3=8 ALIGN=MIDDLE  ALT=\"f%282%29=%282%29%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=8 ALIGN=MIDDLE  ALT=\"f%282%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "# 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y-3=0 ALIGN=MIDDLE  ALT=\"x%2B2y-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y=3 ALIGN=MIDDLE  ALT=\"x%2B2y=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 3 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=3-x ALIGN=MIDDLE  ALT=\"2y=3-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=-x%2B3 ALIGN=MIDDLE  ALT=\"2y=-x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-x%2B3%29%2F2 ALIGN=MIDDLE  ALT=\"y=%28-x%2B3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F2%29x%2B3%2F2 ALIGN=MIDDLE  ALT=\"y=-%281%2F2%29x%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction and simplify.\r<BR>\n" );
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document.write( "We can see that the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%281%2F2%29x%2B3%2F2 ALIGN=MIDDLE  ALT=\"y=-%281%2F2%29x%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F2 ALIGN=MIDDLE  ALT=\"m=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a y-intercept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3%2F2 ALIGN=MIDDLE  ALT=\"b=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now to find the slope of the perpendicular line, simply flip the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F2 ALIGN=MIDDLE  ALT=\"m=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-2%2F1 ALIGN=MIDDLE  ALT=\"m=-2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now change the sign to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the perpendicular slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=-1%2F2 ALIGN=MIDDLE  ALT=\"m=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the coordinates of the given point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(6,-4\right\)\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the point slope formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y--4=2%28x-6%29 ALIGN=MIDDLE  ALT=\"y--4=2%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=6 ALIGN=MIDDLE  ALT=\"x%5B1%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=-4 ALIGN=MIDDLE  ALT=\"y%5B1%5D=-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=y%2B4=2%28x-6%29 ALIGN=MIDDLE  ALT=\"y%2B4=2%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y--4 ALIGN=MIDDLE  ALT=\"y--4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4 ALIGN=MIDDLE  ALT=\"y%2B4\"   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=y%2B4=2x%2B2%28-6%29 ALIGN=MIDDLE  ALT=\"y%2B4=2x%2B2%28-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4=2x-12 ALIGN=MIDDLE  ALT=\"y%2B4=2x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-12-4 ALIGN=MIDDLE  ALT=\"y=2x-12-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-16 ALIGN=MIDDLE  ALT=\"y=2x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "So the equation of the line perpendicular to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y-3=0 ALIGN=MIDDLE  ALT=\"x%2B2y-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(6,-4\right\)\"> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-16 ALIGN=MIDDLE  ALT=\"y=2x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here's a graph to visually verify our answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C-%281%2F2%29x%2B3%2F2%2C2x-16%29%0D%0Acircle%286%2C-4%2C0.08%29%2C%0D%0Acircle%286%2C-4%2C0.10%29%2C%0D%0Acircle%286%2C-4%2C0.12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Graph of the original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2y-3=0 ALIGN=MIDDLE  ALT=\"x%2B2y-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red) and the perpendicular line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-16 ALIGN=MIDDLE  ALT=\"y=2x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green) through the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\(6,-4\right\)\">. \r<BR>\n" );
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document.write( "# 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2By%5E2-6y=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2By%5E2-6y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-8x%29%2B%28y%5E2-6y%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-8x%29%2B%28y%5E2-6y%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-8x%2Bhighlight%2816%29%29%2B%28y%5E2-6y%29=0%2Bhighlight%2816%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-8x%2Bhighlight%2816%29%29%2B%28y%5E2-6y%29=0%2Bhighlight%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take half of the x-coefficient -8 to get -4. Square -4 to get 16. Add this value to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-8x%2B16%29%2B%28y%5E2-6y%2Bhighlight%289%29%29=0%2B16%2Bhighlight%289%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-8x%2B16%29%2B%28y%5E2-6y%2Bhighlight%289%29%29=0%2B16%2Bhighlight%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take half of the y-coefficient -6 to get -3. Square -3 to get 9. Add this value to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y-3%29%5E2=25 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y-3%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y-3%29%5E2=5%5E2 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y-3%29%5E2=5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 25 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2 ALIGN=MIDDLE  ALT=\"5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the equation is in the form <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;\" > (which is a circle) where (h,k) is the center and \"r\" is the radius\r<BR>\n" );
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document.write( "In this case, <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=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <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( "So the center is (4,3) and the radius is 5 units.\r<BR>\n" );
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document.write( "Here's the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C0%29%2C%0D%0Acircle%284%2C3%2C5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );