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Statement : It is possible for a parabola to intersect its directrix.

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Definition of parabola :

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A parabola is the set of all points \"\" that are equidistant from a  fixed line called directrix and a fixed point called the focus  not on the line.

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The directrix of parabola never intersects it.

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From definition of the parabola the statement is false.

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The statement is false.