Equation of Confocal Conics/Formulation 1

Definition
The equation:
 * $\dfrac {x^2} {a^2 + \lambda} + \dfrac {y^2} {b^2 + \lambda} = 1$

where:
 * $\tuple {x, y}$ denotes an arbitrary point in the cartesian plane
 * $a$ and $b$ are (strictly) positive constants
 * $\lambda$ is a (strictly) positive parameter.

defines the set of all confocal conics whose foci are at $...$

Proof
Let $a > c$.

Then from Equation of Confocal Ellipses/Formulation 1, $(1)$ defines the set of all confocal ellipses whose foci are at $...$.

Let $a < c$.

Then from Equation of Confocal Hyperbolas/Formulation 1, $(1)$ defines the set of all confocal hyperbolas whose foci are at $...$.

Hence the result.