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Tangents are drawn to the ellipse (x^2)/...

Tangents are drawn to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1,(a > b),` and the circle `x^2+y^2=a^2` at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) `tan^(-1)((a-b)/(2sqrt(a b)))` (B) `tan^(-1)((a+b)/(2sqrt(a b)))`
(C) `tan^(-1)((2a b)/(sqrt(a-b)))` (D) `tan^(-1)((2a b)/(sqrt(a+b)))`

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