Q13 of 38 Page 723

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

A(p, q) and B(r, s)


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) = (p, q) & (x2, y2) = (r, s)


We get:


(x - p)(x - r) + (y - q)(y - s) = 0


⇒ x2 - rx - px + pr + y2 - sy - qy + qs = 0


⇒ x2 + y2 - (r + p)x - (s + q)y + (pr + qs) = 0


Ans: x2 + y2 - (r + p)x - (s + q)y + (pr + qs) = 0


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