Question

If the circles x² + y² = 9 and x² + y² + 2ax + 2y + 1 = 0 touch each other, then a is :

• A. – 4/3, 4/3
• B. 0
• C. 1
• D. 5/3, –5/3

Answer 1

Answer: (A)

– 4/3, 4/3

Answer 2

Centre of the given circles are C₁(0, 0), C₂(–a, –1)

and their radius are r₁ = 3 and

r₂ = $\sqrt { \mathrm { a } ^ { 2 } + 1 - 1 }$ = a

d = distance between the centres

= C₁C₂ = $\sqrt { \mathrm { a } ^ { 2 } + 1 }$

the given circles touch each other

\ r₁ ± r₂ = d

̃ 3 ± a = $\sqrt { \mathrm { a } ^ { 2 } + 1 }$

̃ 9 + a² ± 6a = a² + 1 ̃ ± 6a = – 8

̃ a = 4/3 or – 4/3