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

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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`

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