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Find the equation of the circle, the coordinates of the end points of one of whose diameters are A(5, - 3) and B(2, - 4)

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The equation of a circle passing through the coordinates of the end points of diameters is: 

(x - x1) (x - x2) + (y - y1)(y - y2) = 0 

Substituting, values:(x1, y1) = (5, - 3) & (x2, y2) = (2, - 4) 

We get: 

(x - 5)(x - 2) + (y + 3)(y + 4) = 0 

⇒ x2 - 2x - 5x + 10 + y2 + 3y + 4y + 12 = 0 

⇒ x2 + y2 - 7x + 7y + 22 = 0 

x2 + y2 - 7x + 7y + 22 = 0

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