Find the equation of the circle?

Question

a diameter of a circle has endpoints (2,3) and (4,5).

Answer 1

The midpoint of the diameter will be the center (h,k)

((x₁+x₂)/2, (y₁+y₂)/2) = ((2+4)/2, (3+5)/2) = (3,4)

 

Center of circle is (h,k) = (3,4)

 

radius is distance from center to either end of diameter.

Distance from (3,4) to (2,3)

r = √[(3-2)²+ (4-3)²] = √2

 

Circle equation:  (x-h)²+(y-k)² = r²

                         (x-3)² + (y-4)² = 2