Question
Can any conic have its focus lying on the corresponding directrix? Give reasons for your answer.
Answer :
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No, a conic section cannot have its focus lying on the corresponding directrix, at least not for a non-degenerate conic section (ellipse, hyperbola, parabola) in Euclidean geometry. The reason lies in the definition of these conic sections:
1. Ellipse: In an ellipse, the distance between the focus and any point on the ellipse is always less than the distance between that point and the directrix.
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