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)
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
Ans: x2 + y2 - 7x + 7y + 22 = 0