x² + y² = ax       ….(1)

Þ   centre                             \({c_1}\left( { - \frac{a}{2},0} \right)\) and radius                             \({r_1} = \left| {\frac{a}{2}} \right|\)

x² + y² = c²                    ….(2)

Þ  centre c₂ (0, 0) and radius r₂ = c

both touch each other iff

|c₁c₂| = r₁ ± r₂

                                  _{\(\frac{{{a^2}}}{4} = {\left( { \pm \frac{a}{2} \pm c} \right)^2} \Rightarrow \frac{{{a^2}}}{4} = \frac{{{a^2}}}{4} \pm |a|c + {c^2} \Rightarrow \,\,|a|\,\, = c\)}