Question

Circle described on any focal chord of a parabola as diameter touches directrix.

• A. True
• B. False

Answer 1

The correct option is A

True

We know that tangents at the extremities of any focal chord intersect at right angles on the directrix.

We also know that the ends of a diameter subtend a right angle on any point on the circle.

$\therefore$ whenever the tangents subtend a right angle the line joining the point of contact of tangents to the parabola can be imagined as the diameter of the circle which would touch the directrix at a point where the tangents intersect.