AB is a diameter of a circle with centre (3, 4). If coordinates of A is the point (4, 9), then find the coordinates of B.

(2, -1)

AB is a diameter of a circle with centre (3, 4).

Coordinates of A is the point (4, 9)

Assume C to be the centre of circle.

AC = sqrt((4-3)^2 + (9-4)^2) = sqrt(1+25) = sqrt(26)

Also AC = BC

Let B be at (x,y)

BC = sqrt((x-3)^2 + (y-4)^2) = sqrt(26)

(x-3)^2 + (y-4)^2 = 26

Applying hit and trial using the given options

(2-3)^2 + (-1-4)^2 = 26

1 + 25 = 26 (The condition is satisfiying the equation)

The correct answer is Option (2) → (2, -1)