Find the equation of the circle, the coordinates of the end points of one of whose diameters are
A(3, 2) and B(2, 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) = (3, 2) & (x2, y2) = (2, 5)
We get:
(x - 3)(x - 2) + (y - 2)(y - 5) = 0
⇒ x2 - 2x - 3x + 6 + y2 - 5y - 2y + 10 = 0
⇒ x2 + y2 - 5x - 7y + 16 = 0
Ans: x2 + y2 - 5x - 7y + 16 = 0