Question
Tangents are drawn to the ellipse and the circle x^{2} + y^{2} = a^{2} at the points where a common ordinate cuts them (on the same side of the xaxis). Then, the greatest acute angle between these tangents is given by




None of these
diffcult
Solution
Let be a point on the ellipse and be the corresponding point on the auxiliary circle x^{2} + y^{2 }= a^{2}. The equations of tangents at P and Q to be respective curves are
Let α be the acute angle between these tangents. Then,
Hence, the greatest values of
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