Question

points A(-1,y) and B(5,7) lie on a circle with center O(2,-3). find the value of y . hence find the radius of the circle.

Answer 1

using midpoint formula , 
[ ( x1+x2 ) /2 , ( y1 +y2 ) /2 ]
substitute the values , 
(2,-3 ) =  [ (-1 + 5 )/2 ,( y+7 ) /2 ]
    now on comparing both LHS and RHS 
   -3 = ( y + 7 ) /2
  -3 × 2 = y + 7 
   -6 = y + 7 
   y = - 6 - 7
 ⇒ y  = -13 
therefore , 
A = ( -1 , -13 ) 

Answer 2

using midpoint formula , 
[ ( x1+x2 ) /2 , ( y1 +y2 ) /2 ] 
substitute the values , 
(2,-3 ) =  [ (-1 + 5 )/2 ,( y+7 ) /2 ]
    now on comparing both LHS and RHS 
   -3 = ( y + 7 ) /2
  -3 × 2 = y + 7 
   -6 = y + 7 
   y = - 6 - 7
 ⇒ y  = -13 
therefore , 
A = ( -1 , -13 )