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Can any conic have its focus lying on the corresponding directrix?Give reasons for your answer

Answer 1

Yes, such a conic section willl be a pair of lines.

You can define conic section as locus of a point which moves so that the ration of its distance from a given point called focus and a given line called directrix is always constant.

In case of ellipse, this ratio is less than #1#, in case of hyperbola, this ratio is more than #1# and in case of parabola, this ratio is exactly #1#.

What happens when focus is on the directrix itself? Consider the following diagram, where #F# is the focus and directrix is line #l_1# so that #F# lies on it. Consider another line #l_2# passing through #F#, so that it forms an angle of #theta# with #l_1#.

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Answer 2

Aaliyah Anderson

No, it is not possible for any conic to have its focus lying on the corresponding directrix. This is because by definition, the focus of a conic lies on the axis of symmetry and is equidistant from the directrix. If the focus were to coincide with the directrix, it would violate this fundamental property of conic sections.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.