Determine the equation of a circle having a diameter with endpoints of (-4,1) and (6,-5).

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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Diameter of the circle `= sqrt((-4-6)^2+(1-(-5))^2) = 2sqrt34`

Radius of the circle `= sqrt34`


Coordinates of the center `= (-4+6)/2,(1+(-5))/2 = (1,-2)`


The equation of a circle having radius r and center (a,b) is given by;

`(x-a)^2+(y-b)^2 = r^2`


So the equation of the circle would be;

`(x-1)^2+(y+2)^2 = 34`