Question

Find the range of values of l for which the variable line 3x+4y-l=0 lies between the circles x²+y²-2x-2y+1=0 and x²+y²-18x-2y+78=0 without intercepting a chord on either circle.

• A. l>21
• B. 12≤l≤21
• C. l<21
• D. Both A and C

Answer 1

The correct option is B

12≤l≤21

The given circle S₁≡ x²+y²-2x-2y+1=0 has centre at C₁ (1, 1) and radius r₁=1.

The other given circle S₂≡ x²+y²-18x-2y+78=0 has centre at C₂(9, 1)and radius r₂ =2.
According to the required condition, we have C₁M₁≥r₁