Circle And System Of Circles Question 17

Question: The two circles $ x^{2}+y^{2}-4y=0 $ and $ x^{2}+y^{2}-8y=0 $

[BIT Ranchi 1985]

Options:

A) Touch each other internally

B) Touch each other externally

C) Do not touch each other

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

$ r_1=2 $ ; $ r_2=4 $

$ C_1C_2=2 $

$ \because \ r_2-r_1=C_1C_2 $

$ \therefore $ Circle touches internally.