Question

The graph of the equation below is a circle. What is the length of the radius of the circle? (x - 4)^2 + (y + 12)^2 = 17^2

Answer 1

The correct answer is:  [D]:  "17" .
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The radius is:  " 17" .
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Note:
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The formula/equation for the graph of a circle is:
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   (x − h)²  +  (y − k)² =  r²  ;

in which:  

          " (h, k) " ; are the coordinate of the point of the center of the circle;

           "r" is the length of the "radius" ; for which we want to determine;
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We are given the following equation of the graph of a particular circle:
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          →  (x − 4)²  +  (y + 12)² =  17² ;

which is in the correct form:

→  " (x − h)²  +  (y − k)² =  r²  " ;

 in which:  " h = 4 " ;

                  " k = -12" ;

                   "r = 17 " ;  which is the "radius" ; which is our answer.

          →  { Note that: "k = NEGATIVE  12" } ;

→  Since the equation for this particular circle contains the expression:             _________________________________________________________    
                      →     "...(y + k)² ..." ;  
         
[as opposed to the standard form:  "...(y − k)² ..." ] ; 
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→  And since the coordinates of the center of a circle are represented by:
            " (h, k) " ;  
 
→  which are:  " (4, -12) " ;  (for this particular circle) ; 
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→  And since:  " k = -12 " ;  (for this particular circle) ;
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then: 

 " [y − k ] ²  =  [ y − (k) ] ²  =  " [ y − (-12) ] ² " ;
                                    
                                         =  " ( y + 12)² "  ;
                                    
{NOTE:  Since:  "subtracting a negative" is the same as "adding a positive" ;

           →   So;  " [ y − (-12 ] " = " [ y + (⁺ 12) ] " = " (y + 12) "
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Note:  The above explanation is relevant to confirm that the equation is, in fact, in "proper form"; to ensure that the:  radius, "r" ;  is:  "17" .
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           →    Since:  "r  =  17 " ;  

           →  The radius is:  " 17 " ;

          which is:  Answer choice:  [D]:  "17" .
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Answer 2

(x - 4)^2 + (y + 12)^2 = 17^2
r = 17 because radicand 289 is 17