Question

The circle described on any focal chord of a parabola as diameter touches the directrix.

• A. True
• B. False

Answer 1

The correct option is A True

Let $A$ and $B$ the ends of focal chord.

Circle is drawn taking $AB$ as diameter.

So as diameter is semi major chord.

Angle subtended by diameter at angle point of circle is same ie. ${90}^{\circ }$.

As we know tangent drawn at$AB$ (ends of focal chord) are always perpendicular and meet at directrix. So, we can claim that circle drown taking $AB$ are diameter touches directrix of parabola.