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Prove that the chord of contact of the e...

Prove that the chord of contact of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` with respect to any point on the directrix is a focal chord.

Text Solution

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Variable point on the directrix can be taken as P(a|e,k), `k in R`.
Eqaution of chord of contact of the ellipse w.r.t. this point is
`((a//e)x)/(a^(2))+(ky)/(b^(2))=1`
Clearly, focus S (ae ,0) stasfies the above line.
Hence. Proved
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