Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).

Let the coordinates of A be (x, y).
AB is a diameter of the circle then Midpoint of AB is center of the circle which is (2, -3).
Mid point of A and B = (x1+x2/2, y1+y2/2)
∴ (2, -3) = (x+1/2, y+4/2)
⇒ x+1/2 = 2 ⇒ x+1 = 4 ⇒ x = 3
⇒ y+4/2 = -3 ⇒ y+4 = -6; ⇒ y = -10
∴ Coordinates of A is (3, -10).