Question

Which of the following is/are True? The circles x² + y² – 6x – 6y + 9 = 0 and x² + y² + 6x + 6y + 9 = 0 are such that 

(A) They do not intersect. 

(B) They touch each other. 

(C) Their direct common tangents are parallel. 

(D) Their trannsverse common tangents are perpendicular.

Answer 1

Correct option  (A, C, D)

Explanation:

They do not intersect with each other 

Since their radius are same 

∴ External direct common tangents are parallel 

Also, the point of intersection of transverse common tangents is midpoint of C₁ and C₂ (same radii)

Angle between tangents = 2θ = 90º