Center of a circle is a midpoint of line connecting two endpoints so center is: (12,-14) (2,4) we divide those two points by two C(a,b)- center C(a,b)=((12+2)/2),(-14+4)/2)=(7,-5) Radius is the distance from the center to any point on the circle: we take point (2,4) r= ( 7 − 2 ) 2 + ( − 5 − 4 ) 2 = 25 + 81 = 106
The equation of the circle with a diameter defined by the endpoints (12, -14) and (2, 4) is ( x − 7 ) 2 + ( y + 5 ) 2 = 106 . This was derived by calculating the midpoint to find the center and then using the distance formula to find the radius. Finally, the standard form of the circle equation was applied.
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