If two concentric ellipses of eccentricities  e,e¹ are such that the foci of one of ellipse lies on other , and their length of major axes are equal and 
S₁: If the angle between their major axes of ellipse is $\mathrm{\theta }$   then  $\mathrm{sin\theta }=\sqrt{\left(1-\frac{1}{{\mathrm{e}}^2}\right)\left(1-\frac{1}{{\mathrm{e}}^{1^2}}\right)}$
S₂: The quadrilateral formed by joining the foci of two ellipse is a parallelogram, then