If M and m are the maximum and minimum values of y x for pair of real numbers x , y which satisfy the equation x - 3 2 + y - 3 2 = 6 , then the value of 1 M + 1 m is

Step-by-step solution

Let y x = m ' . So, on putting y = m ′ x in the given circle, We get x − 3 2 + m ′ x − 3 2 = 6 ⇒ x 2 1 + m ' 2 - 6 x 1 + m ' + 12 = 0 Putting discriminant = 0 , we get, m ' = 3 + _ 2 2 So, m = 3 - 2 2 and M = 3 + 2 2 ⇒ m M = 1 ⇒ 1 M + 1 m = m + M = 3 - 2 2 + 3 + 2 2 = 6