Find the standard form of the equation of the circle with en

Find the standard form of the equation of the circle with endpoints of diameter at the points (7, 4) and (-9, 2). Type the standard form of the equation of this circle.

Solution

Circle with end points of diameter (7,4), (-9,2)

Centre of circle (h,k) = mid point of diameter = [ (7-9)/2 , (4+2) /2] = (-1,3)

diameter = length of (7,4), (-9,2)

              = [ (7+9)² + (4-2)²]^1/2

             = (260)^1/2

                 = 2 (65)^1/2

radius r = diameter/2 = 2 (65)^1/2 / 2 = (65)^1/2

Therefore, standard form of circle is

   (x-h)² + (y-k)² = r²

(x+1)² + (y-3)² = 65