Question

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

Answer 1

Let the centre of the circle be O. 
Since AB is the diameter so, O is the midpoint of AB.
Thus, using the section formula,

`("a" +1)/2 = 2`

⇒ a = 4 - 1 = 3

and

`("b" + 4)/2 = -3`

⇒ b = - 10

So, the coordinate of point A is (3 , -10)