Question

The two circles x² + y² – 2x – 4y = 0 and x² + y² – 8y – 4 = 0

(1) Intersect each other 

(2) Touch each other internally

(3) Touch each other externally 

(4) None of the

Answer 1

(2) Touch each other internally

Explanation

For first circle x² + y² – 2x – 4y = 0

Centre C₁ ≡ (1, 2) and radius 

and for the second circle  x² + y² – 8y – 4 = 0

Centre C₂ ≡ (0, 4) and radius

Thus, two circles touch each other internally.