Question

Let C1: x2 + y2 = 4 and C2: x2 + y2 - 6x - 8y - 24 = 0. Then

(A) C1 and C2 touch each other internally

(B) C1 and C2 do not intersect

(C) the number of common tangents is 2

(D) the number of common tangents is 1

Answer 1

Correct option (a,d)

Explanation :

We have

A = (0,0) and r1 = 2

B = (3,4) and r2 = 7

Now, AB = 5 = 7 - 2 = r2 - r1 . Therefore, the two circles C1 and C2 touch each other internally and hence they have only one common tangent.