document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193536>Question 1193536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Find an equation of a circle passing through the points A(1,2) and B(1,-2) touching the line x+2y+5=0.\r<BR>\n" );
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document.write( "2. Find the center and radius of 5x^2+5y^2+24+36y+10=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825590 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor answered your second question, which is rather basic.<br><BR>\n" );
document.write( "Your first question is much more interesting.<br><BR>\n" );
document.write( "The circle passes through A(1,2) and B(1,-2), so AB is a chord of the circle.<br><BR>\n" );
document.write( "The perpendicular bisector of any chord of a circle passes through the center of the circle; the perpendicular bisector of AB is the x-axis. So the center of the circle is (a,0).<br><BR>\n" );
document.write( "(1) The radius of the circle is the distance from (a,0) to (1,2).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%28%28a-1%29%5E2%2B2%5E2%29=sqrt%28a%5E2-2a%2B5%29 ALIGN=MIDDLE  ALT=\"r=sqrt%28%28a-1%29%5E2%2B2%5E2%29=sqrt%28a%5E2-2a%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(2) The radius of the circle is also the (shortest) distance from (a,0) to the line x+2y+5=0.<br><BR>\n" );
document.write( "The shortest distance from a point (p,q) to a line with equation Ax+By+C=0 is given by the formula<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28Ap%2BBq%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29 ALIGN=MIDDLE  ALT=\"abs%28%28Ap%2BBq%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "For this problem the distance from (a,0) to the line x+2y+5=0 is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28%28%28a%29%281%29%2B2%280%29%2B5%29%2Fsqrt%281%5E2%2B2%5E2%29%29=abs%28%28a%2B5%29%2Fsqrt%285%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Square both expressions for the radius and set them equal to each other to solve for a.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-2a%2B5=%28%28a%2B5%29%5E2%2F5%29 ALIGN=MIDDLE  ALT=\"a%5E2-2a%2B5=%28%28a%2B5%29%5E2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-2a%2B5=%28a%5E2%2B10a%2B25%29%2F5 ALIGN=MIDDLE  ALT=\"a%5E2-2a%2B5=%28a%5E2%2B10a%2B25%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a%5E2-10a%2B25=a%5E2%2B10a%2B25 ALIGN=MIDDLE  ALT=\"5a%5E2-10a%2B25=a%5E2%2B10a%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%5E2-20a=0 ALIGN=MIDDLE  ALT=\"4a%5E2-20a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28a%29%28a-5%29=0 ALIGN=MIDDLE  ALT=\"4%28a%29%28a-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "There appear to be 2 solutions; a=0 or a=5.<br><BR>\n" );
document.write( "If a=0, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=abs%285%2Fsqrt%285%29%29=sqrt%285%29 ALIGN=MIDDLE  ALT=\"r=abs%285%2Fsqrt%285%29%29=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the equation of the circle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=5 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If a=5, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=abs%28%285%2B5%29%2Fsqrt%285%29%29=10%2Fsqrt%285%29=2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"r=abs%28%285%2B5%29%2Fsqrt%285%29%29=10%2Fsqrt%285%29=2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the equation of the circle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2By%5E2=20 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2By%5E2=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph, showing the line x+2y+5=0 and the two circles tangent to it that both pass through the given point (1,2) and (1,-2):<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-6%2C10%2C-6%2C10%2C-.5x-2.5%2Csqrt%285-x%5E2%29%2C-sqrt%285-x%5E2%29%2Csqrt%2820-%28x-5%29%5E2%29%2C-sqrt%2820-%28x-5%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );