document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768566>Question 768566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A and B are the points of intersection of the circle with equation x^2 + y^2 + 4x - 6y + 9 =0 and the diameter passing through origin. Find the coordinates of A and B.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468391 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=468391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A and B are the points of intersection of the circle with equation x^2 + y^2 + 4x - 6y + 9 =0 and the diameter passing through origin. Find the coordinates of A and B.<BR>\n" );
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document.write( "Find the center and radius of the circle.<BR>\n" );
document.write( "x^2 + y^2 + 4x - 6y + 9 =0<BR>\n" );
document.write( "x^2 + y^2 + 4x - 6y = -9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2+%2B+%28y-3%29%5E2+=+4 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2+%2B+%28y-3%29%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Center at (-2,3), r = 2<BR>\n" );
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document.write( "Equation of the line thru the center and the Origin is<BR>\n" );
document.write( "y = -3x/2<BR>\n" );
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document.write( "Sub for y in the eqn of the circle.<BR>\n" );
document.write( "x^2 + y^2 + 4x - 6y + 9 = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%289x%5E2%29%2F4+%2B+4x+%2B+9x+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%289x%5E2%29%2F4+%2B+4x+%2B+9x+%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%5E2%2F4+%2B+13x+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"13x%5E2%2F4+%2B+13x+%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.25x%5E2%2B13x%2B9+=+0 ALIGN=MIDDLE  ALT=\"3.25x%5E2%2B13x%2B9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2813%29%5E2-4%2A3.25%2A9=52 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2813%29%5E2-4%2A3.25%2A9=52\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=52 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-13%2B-sqrt%28+52+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-13%2B-sqrt%28+52+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+52+%29%29%2F2%5C3.25+=+-0.890599607549542 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+52+%29%29%2F2%5C3.25+=+-0.890599607549542\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2813%29-sqrt%28+52+%29%29%2F2%5C3.25+=+-3.10940039245046 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2813%29-sqrt%28+52+%29%29%2F2%5C3.25+=+-3.10940039245046\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.25x%5E2%2B13x%2B9 ALIGN=MIDDLE  ALT=\"3.25x%5E2%2B13x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.25x%5E2%2B13x%2B9+=+%28x--0.890599607549542%29%2A%28x--3.10940039245046%29 ALIGN=MIDDLE  ALT=\"3.25x%5E2%2B13x%2B9+=+%28x--0.890599607549542%29%2A%28x--3.10940039245046%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.890599607549542, -3.10940039245046.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3.25%2Ax%5E2%2B13%2Ax%2B9+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3.25%2Ax%5E2%2B13%2Ax%2B9+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2+%2B-sqrt%28208%29%2F13 ALIGN=MIDDLE  ALT=\"x+=+-2+%2B-sqrt%28208%29%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use y = -3x/2 to find the y's of A and B\r<BR>\n" );
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