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I have heard about the theorem that tangents drawn at the extremities of the focal chord intersect on the directrix. Is the converse of the theorem also true ? i.e., is the following statement true “If two tangents drawn to a parabola are at right angles to each other , their chord of contact will always be the focal chord”? I know that the locus of the point of intersection of perpendicular tangents to a parabola is called the director’s circle, so obviously , any perpendicular tangents will always intersect in the directors circle.

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    $\begingroup$ yes the statement in inverted commas is true, but the notion of a Director Circle applies to the ellipse. For a parabola, the locus of intersection points of perpendicular tangents is the directrix. $\endgroup$ – David Quinn Mar 31 '18 at 11:55
  • $\begingroup$ @David alright ! Thank you ! $\endgroup$ – Aditi Mar 31 '18 at 12:47

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