document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=769839>Question 769839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the equation of the circle in general form with a radius r = 5 if the line x- 2y - 1 = 0 is a tangent to this circle at a point (3,1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #469073 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=469073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the given line and the included point, and find the line which is perpendicular at that given point.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y-1=0 ALIGN=MIDDLE  ALT=\"x-2y-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=-x%2B1 ALIGN=MIDDLE  ALT=\"-2y=-x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x-%281%2F2%29 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x-%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the given line.\r<BR>\n" );
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document.write( "The line perpendicular to the given line will have slope -2, which is negative reciprocal of the (1/2).  We not yet know the y intercept, b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2Bb ALIGN=MIDDLE  ALT=\"y=-2x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%2B2x ALIGN=MIDDLE  ALT=\"b=y%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which must contain the point given, (3,1).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%281%29%2B2%283%29 ALIGN=MIDDLE  ALT=\"b=%281%29%2B2%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The line we look for is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B7 ALIGN=MIDDLE  ALT=\"y=-2x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We have a set of points based on this wanted and found line, (x, -2x+7)<BR>\n" );
document.write( "and a particular point, (3, 1) and we want the distance between them to be 5, which is the radius of the wanted circle.  Note again, (3,1) is a point on this circle.\r<BR>\n" );
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document.write( "DISTANCE FORMULA!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-3%29%5E2%2B%28-2x%2B7-1%29%5E2%29=5 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-3%29%5E2%2B%28-2x%2B7-1%29%5E2%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x%5E2-6x%2B9%29%2B%28-2x%2B6%29%5E2%29=5 ALIGN=MIDDLE  ALT=\"sqrt%28%28x%5E2-6x%2B9%29%2B%28-2x%2B6%29%5E2%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2-6x%2B9%2B%284x%5E2-24x%2B36%29%29=5 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2-6x%2B9%2B%284x%5E2-24x%2B36%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285x%5E2-30x%2B45%29=5 ALIGN=MIDDLE  ALT=\"sqrt%285x%5E2-30x%2B45%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Square both sides...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2-30x%2B45=5 ALIGN=MIDDLE  ALT=\"5x%5E2-30x%2B45=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B9=1 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-6x%2B8=0 ALIGN=MIDDLE  ALT=\"x%5E2-6x%2B8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >____________This will give an x-coordinate for the center of the circle.\r<BR>\n" );
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document.write( "Use general solution to quadratic formula to find the value of the x-coordinate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%286%2B-sqrt%2836-4%2A8%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%286%2B-sqrt%2836-4%2A8%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2B-2%29%2F2 ALIGN=MIDDLE  ALT=\"x=6%2B-2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the line equation found, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2B7 ALIGN=MIDDLE  ALT=\"y=-2x%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to find either or both y-coordinates for the center of the circle.<BR>\n" );
document.write( "x=2:<BR>\n" );
document.write( "y=-2*2+7<BR>\n" );
document.write( "y=3<BR>\n" );
document.write( "so one possible center point is (2,3).<BR>\n" );
document.write( "x=4:<BR>\n" );
document.write( "y=-2*4+7<BR>\n" );
document.write( "y=-1<BR>\n" );
document.write( "so other possible center point is (4, -1).\r<BR>\n" );
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document.write( "You asked for help including \"general form\" for the circle, but I'll just finish this in \"standard form\", and you can convert if you want.\r<BR>\n" );
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document.write( "Standard form of your circle is <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;\" > in which the center point is (h, k).  You have two possible points to choose from.<BR>\n" );
document.write( "Either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-2%29%5E2%2B%28y-3%29%5E2=25%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-2%29%5E2%2B%28y-3%29%5E2=25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-4%29%5E2%2B%28y%2B1%29%5E2=25%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-4%29%5E2%2B%28y%2B1%29%5E2=25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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