An ellipse $\text{ (E) }\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}+\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$, centered at point O have AB and CD as its major and minor axes, respectively, let S₁ be one of the foci of the ellipse, radius of incircle of triangle OCS₁ be 1 unit and OS₁ = 6 units.