Question 216628
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
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(1) for (4,5) this  becomes,,,,(4-h)^2 +(5-k)^2 = r^2
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(2) for (-2,3) this becomes,,,,(-2-h)^2 +(3-k)^2 = r^2
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(3) for (-4,-3) this  becomes,,,(-4-h)^2 + (-3-k)^2 =r^2
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with  3 unknowns  and  3 equations,  we  can  solve  for  h,k,&r
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However,  this  is  a  lot  of  work,,,,A  rough sketch  on  graph  paper helps
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Reviewing  the  answers,  we  find
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a) (5,-4) @r=7
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b) (3,-2) @ r=sqrt50
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c) (-4,2) @ r= 6
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d) (2,-2) @ r=5
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from  sketch  (b) is  most  likely,,,,(radius  fits)
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subst in  each  of  the  3  above  eqns  confirms  that  (b)  is  the  answer
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for  example,  subst  (3,-2) @ r=sqrt50 in  eqn  (1)
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{4-(3)}^2 +{5-(-2)}^2 = (sqrt50)^2
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1^2 +7^2 =50
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1+49 =50,,,,,ok
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Likewise  for  all  3  eqns,,,,,honest
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