The radius of a circle, having minimum area, which touches the curve y = 4 - x 2 and the lines, y = x is:

Step-by-step solution

Length of perpendicular from centre of circle to tangent line r = k 2 And r = 4 - k   ⇒     r = 4 - k = k 2 ⇒ 4 = k + 2 k 2 ⇒   k = 4 2 2 + 1 ⇒ r = 4 2 2 + 1 2 ⇒ r = 4 2 + 1   ⇒       r = 4 2 - 1