Find the coordinates of a point A, where AB is a diameter of the circle whose centre is (2, -3) and B is (1, 4).
Here given that AB is a diameter of the circle whose centre is (say) C(2, -3) and B is (1, 4)
Let A be (x, y)
We know that as C is center, AC = CB or C is midpoint of AB.
By midpoint formula,
x = , y =
For Center C,
2 = and -3 =
∴ x = 4 – 1 and y = -6 – 4
∴ x = 3 and y = -10
Hence, coordinates of A are (3, -10)