If a circle C , whose radius is 3 , touches externally the circle x 2 + y 2 + 2 x - 4 y - 4 = 0 at the point 2 , 2 , then the length of the intercept cut by this circle C on the x -axis is equal to

Step-by-step solution

The equation of a tangent to the given circle at 2 , 2 is x 2 + y 2 + x +2 −2 y +2 −4=0⇒3 x −6=0⇒ x =2 Family of the circle touching a given line at a given point x - 2 2 + y - 2 2 + λ x - 2 = 0 . ⇒ x 2 + y 2 + λ − 4 x − 4 y + 8 − 2 λ = 0 Radius = 3 = λ − 4 2 2 + 4 − 8 − 2 λ ⇒ 9 = λ 2 − 8 λ + 16 4 − 4 + 2 λ ⇒ 36 = λ 2 − 8 λ + 16 − 16 + 8 λ ⇒ λ