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A circle is drawn to pass through the ex...

A circle is drawn to pass through the extremities of the latus rectum of the parabola `y^2=8xdot` It is given that this circle also touches the directrix of the parabola. Find the radius of this circle.

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The correct Answer is:
4
The extremities of the latus rectum are (2,4) and (2,-4).
Since any circle drawn with any focal chord as its diameter touches the directrix, the radius of the circle is 2a=4 (sincea=2).
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