Circle 2 Question 11

12. The number of common tangents to the circles x2+y2=4 and x2+y26x8y=24 is

(1998,2M)

(a) 0

(b) 1

(c) 3

(d) 4

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Answer:

Correct Answer: 12. (a)

Solution:

  1. Given, x2+y2=4

Centre C1(0,0) and R1=2

Again, x2+y26x8y24=0, then C2(3,4)

and

R2=7

Again,

C1C2=5=R2R1

Therefore, the given circles touch internally such that, they can have just one common tangent at the point of contact.



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