Question

The number of common tangents to the circles x² + y² - 2x   - 6y + 9 = 0 and x² + y² + 6x -2y + 1 = 0 is

(A)  4

(B)  3

(C)  2

(D)  1

Answer 1

Correct option  (A)  4

Explanation :

A = (1, 3) and r₁ = 1, respectively, are the centre and the radius of the first circle. B = (3, 1) and r₂ = 3, respectively, are the centre and radius of the second circle. So

 

Therefore, the two circles do not have a common point. Hence, the number of common tangents is 4.