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# Let P be any point on any directrix of an ellipse Then the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at

- some point on the major axis depending upon the position of point P
- the midpoint of the line segment joining the center to the corresponding focus
- the corresponding focus
- none of these

## The correct answer is: the corresponding focus

### Given that Let P be any point on any directrix of an ellipse Then we need to find the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at what point

which are family of concurrent lines passing through point $(ae,0)$ i.e. focus of ellipse

Therefore, the chords of contact of point P with respect to the ellipse and its auxiliary circle intersect at the corresponding focus.

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