Question

The circles (x–a)² +(y–b)² = c² and (x–b)² +(y–a)² = c² touch each other, then

(a) a=b ± 2c

(b) a = b ± √2c

(c) a = b ± c

(d) None of these

Answer 1

Distance between centres = |r₁ ± r₂|

Distance between (a,b) and (b,a) = |2c| or 0

\(\sqrt{(a-b)^2+(b-a)^2}\) = ± 2c

√2 (a–b) = ± 2c

a–b = ± √2 c

a=b ± √2 c