Circle(s) touching x -axis at a distance 3 from the origin and having an intercept of length 2 7 on y -axis is (are)

Step-by-step solution

Let the circle be x 2   +   y 2   +   2 g x   +   2 f y   +   c   =   0 According to the question, g 2 - c = 0 ⇒ g 2 = c   . . . . i and 2 f 2 - c = 2 7 ⇒ f 2 - c = 7 . . . . . i i The circle passes through the point 3 ,   0 , then 9 + 0 + 6 g + 0 + c = 0 ⇒ 9 + 6 g + g 2 = 0 , by i ⇒ ( g + 3 ) 2 = 0 ⇒ g = - 3 ∴   c   =   9 and f 2   =   16   ⇒ f = ± 4 So the required circles are x