document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=714400>Question 714400</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the center, radius, and intercepts of the circle with the given equation x^2+y^2+10y-24=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #438799 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=438799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The intercepts will be when x=0 and you solve for y, and when y=0 and you solve for x.  Both situations will give you quadratic equation in one variable. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2A0%2By%5E2%2B10y-24=0 ALIGN=MIDDLE  ALT=\"0%2A0%2By%5E2%2B10y-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B10y-24=0 ALIGN=MIDDLE  ALT=\"y%5E2%2B10y-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > for whe x=0.  Easily factorable to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-2%29%28y%2B12%29=0 ALIGN=MIDDLE  ALT=\"%28y-2%29%28y%2B12%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so intercepts will be at y=2 and y=-12.  So see how that works?  You can do the same for finding the intercepts when y=0.\r<BR>\n" );
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document.write( "Finding radius and center need a different equation form.  Put the equation into standard form by Completing the square.  Do this for BOTH variables.\r<BR>\n" );
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document.write( "Here's getting the process started.<BR>\n" );
document.write( "x^2+y^2+10y-24=0<BR>\n" );
document.write( "x is already in good shape.  No need to complete the square for x.  y needs some work.<BR>\n" );
document.write( "The square term to add and subtract is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2F2%29%5E2=25 ALIGN=MIDDLE  ALT=\"%2810%2F2%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%2B10y%2B25%29-25=%28y%2B5%29%5E2-25 ALIGN=MIDDLE  ALT=\"%28y%5E2%2B10y%2B25%29-25=%28y%2B5%29%5E2-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  We now must include that in the original equation:\r<BR>\n" );
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document.write( "Putting that result into the original equation, we obtain:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B+%28y%2B5%29%5E2-25+-24+=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B+%28y%2B5%29%5E2-25+-24+=0\"   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%5E2%2B%28y%2B5%29%5E2=49%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2B%28y%2B5%29%5E2=49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OR<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5E2%2B%28y%2B5%29%5E2=7%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5E2%2B%28y%2B5%29%5E2=7%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Center is at (0,-5) and radius is 7. </SPAN>\n" );
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