Equation

The end points of a circle's diameter are (-2, 2),(4,8). What is the equation, in standard form, for this circle?
First find the length of the diameter by using the distance formulae.

d = √[(x2 - x1)2 + (y2 - y1)2]

d = √[(4 - (-2))2 + (8 - 2)2] = √72 = 6√ 2

The radius is the diameter divided by 2. The radius = (6√ 2)/2 = 3√ 2

Next we need the center of the circle which is the midpoint of the diameter.

midpoint =  
  
x2 + x1   
2
   
y2 + y1   
2
  
4 + (-2)   
2
   
8 + 2   
2

The center of the circle is the diameter's midpoint = (1, 5) These are the (h, k) values in the standard equation.

  The equation for the standard circle is; (x - h)2 + (y - k)2 = r2

substitute in the (h, k) values:    (x - 1)2  +  (y - 5)2  =  (3√ 2)2

   (x - 1)2  +  (y - 5)2  =  18    and this is the answer for question # 50


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