Let C: x^2+y^2=4 and C^′: x^2+y^2-4 λ x+9=0 be two circles. If the set of all values of λ so that the circles C and C^′ intersect at two distinct…

Let $\displaystyle C: x^2+y^2=4$ and $\displaystyle C^{\prime}: x^2+y^2-4 \lambda x+9=0$ be two circles. If the set of all values of $\displaystyle \lambda$ so that the circles C and $\displaystyle \mathrm{C}^{\prime}$ intersect at two distinct points, is $\displaystyle \mathrm{R}-[\mathrm{a}, \mathrm{b}]$, then the point $\displaystyle (8 \mathrm{a}+12,16 \mathrm{~b}-20)$ lies on the curve: