document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158183>Question 1158183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For (a), find center and radius. For (b), explain why it has the same graph as (a).<BR>\n" );
document.write( "(a) (x−5)^2 +(y+3)^2 =49<BR>\n" );
document.write( " (b) x^2 −10x+y^2 +6y=15 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781126 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781126\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "For (a), find center and radius. For (b), explain why it has the same graph as (a).<BR>\n" );
document.write( "(a)\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2+%2B%28y%2B3%29%5E2+=49 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2+%2B%28y%2B3%29%5E2+=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "find center and radius: compare to  <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;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > are coordinates of the center, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is radius\r<BR>\n" );
document.write( "\n" );
document.write( " => in your case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=5 ALIGN=MIDDLE  ALT=\"h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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;\" >=> the center is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%2849%29=7 ALIGN=MIDDLE  ALT=\"r=sqrt%2849%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(b) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10x%2By%5E2+%2B6y=15 ALIGN=MIDDLE  ALT=\"x%5E2-10x%2By%5E2+%2B6y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to explain why it has the same graph as (a), write it in <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;\" > form\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-10x%29%2B%28y%5E2+%2B6y%29=15 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%29%2B%28y%5E2+%2B6y%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....complete squares\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-10x%2Bb%5E2%29-b%5E2%2B%28y%5E2+%2B6y%2Bb%5E2%29-b%5E2+=15 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%2Bb%5E2%29-b%5E2%2B%28y%5E2+%2B6y%2Bb%5E2%29-b%5E2+=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >...for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=10%2F2=5 ALIGN=MIDDLE  ALT=\"b=10%2F2=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6%2F2=3 ALIGN=MIDDLE  ALT=\"b=6%2F2=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-10x%2B5%5E2%29-5%5E2%2B%28y%5E2+%2B6y%2B3%5E2%29-3%5E2+=15 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%2B5%5E2%29-5%5E2%2B%28y%5E2+%2B6y%2B3%5E2%29-3%5E2+=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2-25%2B%28y+%2B3%29%5E2-9+=15 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2-25%2B%28y+%2B3%29%5E2-9+=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2B%28y+%2B3%29%5E2-34+=15 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y+%2B3%29%5E2-34+=15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2B%28y+%2B3%29%5E2+=15%2B34 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y+%2B3%29%5E2+=15%2B34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2%2B%28y+%2B3%29%5E2+=49 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y+%2B3%29%5E2+=49\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> proof that equation is same as equation in (a), therefore both have the same graph\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );