A circle ‘C’ touch the transverse axis at a focus S of the hyperbola  $\frac{x^2}{4}-\frac{y^2}{3}=1$, and pass through one end of the conjugate axis $[i.e(0,b),b>0]$ Another circle ‘D’ touch the transverse axis at a focus S’ of the hyperbola $\frac{x^2}{4}-\frac{y^2}{3}=1$ , and pass through same end of the conjugate axis $[i.e(0,b),b>0]$ 

Both the circles C and D intersect at E and F . 

Then which of the following is /are true