document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=216628>Question 216628</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write the standard form of the equation of the circle that passes through the points at (4,5),(-2,3), and (-4,-3).\r<BR>\n" );
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document.write( "a)(x-5)^2 + (y+4)^2 = 49<BR>\n" );
document.write( "b)(x-3)^2 + (y+2)^2 = 50<BR>\n" );
document.write( "c)(x+4)^2 + (y-2)^2 = 36<BR>\n" );
document.write( "d)(x-2)^2 + (y+2)^2 = 25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #163573 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=163573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The  formal  method  of  solution  is  to  start  with  the  basic  eqn  of  a  circle,,(x-h)^2 +(y-k)^2 = r^2,  where  center  is  (+h,+k) and  radius  is  r<BR>\n" );
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document.write( "(1) for (4,5) this  becomes,,,,(4-h)^2 +(5-k)^2 = r^2<BR>\n" );
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document.write( "(2) for (-2,3) this becomes,,,,(-2-h)^2 +(3-k)^2 = r^2<BR>\n" );
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document.write( "(3) for (-4,-3) this  becomes,,,(-4-h)^2 + (-3-k)^2 =r^2<BR>\n" );
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document.write( "with  3 unknowns  and  3 equations,  we  can  solve  for  h,k,&r<BR>\n" );
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document.write( "However,  this  is  a  lot  of  work,,,,A  rough sketch  on  graph  paper helps<BR>\n" );
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document.write( "Reviewing  the  answers,  we  find<BR>\n" );
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document.write( "a) (5,-4) @r=7<BR>\n" );
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document.write( "b) (3,-2) @ r=sqrt50<BR>\n" );
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document.write( "c) (-4,2) @ r= 6<BR>\n" );
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document.write( "d) (2,-2) @ r=5<BR>\n" );
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document.write( "from  sketch  (b) is  most  likely,,,,(radius  fits)<BR>\n" );
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document.write( "subst in  each  of  the  3  above  eqns  confirms  that  (b)  is  the  answer<BR>\n" );
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document.write( "for  example,  subst  (3,-2) @ r=sqrt50 in  eqn  (1)<BR>\n" );
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document.write( "{4-(3)}^2 +{5-(-2)}^2 = (sqrt50)^2<BR>\n" );
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document.write( "1^2 +7^2 =50<BR>\n" );
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document.write( "1+49 =50,,,,,ok<BR>\n" );
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document.write( "Likewise  for  all  3  eqns,,,,,honest<BR>\n" );
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