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).

Find the coordinates of a point A, where AB is a diameter of a circle with center C (2, -3) and the other end of the diameter is B (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

⇒ a = 3

and

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

⇒ b = -10

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

Answer 2

C (2, -3) is the center of the given circle. Let A(a, b) and B(1, 4) be the two end-points of the given diameter AB. Then, the coordinates of C are

`x = (a+1)/2 , y =( b+4)/2`

It is given that x = 2 and y = -3

⇒ `2= (a+1)/2, 3 = (b+4)/2`

⇒ 4 = a + 1, -6 = b + 4 

⇒ a = 4 - 1, b = -6 - 4

⇒ a = 3, b = -10

Therefore, the coordinates of point A are (3, -10).