The diameter of the circle, whose Centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2 is

Step-by-step solution

Centre of circle lies on the line x + y = 2 . Any point on the line can be assumed as α ,   2 - α . So let Centre of circle is α ,   2 - α . Since both lines x = 3 and y = 2 touches the circle means distance from the Centre of circle to the line is equal to radius. Let r is radius of circle. For the line x = 3   ⇒ x - 3 = 0 r = α - 3 1 = α - 3     . . . 1 For the line y = 2   ⇒ y - 2 = 0 r = 2 - α - 2 1 = α     . . . 2 From