The common tangent to the circles x 2 + y 2 = 4 and x 2 + y 2 + 6 x + 8 y - 24 = 0 also passes through the point:

Step-by-step solution

The centre and radius of the circle x 2 + y 2 + 2 g x + 2 f y + c = 0 are respectively - g ,   - f and g 2 + f 2 - c . Let, for the circle S 1 : x 2 + y 2 = 4 centre C 1 : 0 ,   0 ,   r 1 = 2 units. And, for the circle S 2 : x 2 + y 2 + 6 x + 8 y - 24 = 0 centre C 2 - 3 ,   - 4 ,   r 2 = 3 2 + 4 2 + 24 = 7 units. The distance between the points x 1 ,   y 1 and x 2 ,   y 2 is x 1 - x 2 2 + y 1 - y 2 2 Hence, the distance between the centres of the circles is C 1 C 2 = - 3 - 0 2 + -