Find the equation of the circle, the coordinates of the end points of one of whose diameters are

A( - 2, - 3) and B( - 3, 5)


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) = ( - 2, - 3) & (x2, y2) = ( - 3, 5)


We get:


(x + 2)(x + 3) + (y + 3)(y - 5) = 0


⇒ x2 + 3x + 2x + 6 + y2 - 5y + 3y - 15 = 0


⇒ x2 + y2 + 5x - 2y - 9 = 0


Ans: x2 + y2 + 5x - 2y - 9 = 0


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