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From any point on any directrix of the e...

From any point on any directrix of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1,a > b ,` a pari of tangents is drawn to the auxiliary circle. Show that the chord of contact will pass through the correspoinding focus of the ellipse.

Text Solution

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Let the point of the directrix be (a/e,k)
Then the equation of AB will be `x((a)/(e))+yk=a^(2)`
Now, it will clearly pass through the focus of the ellipse as `(ae)((a)/(e))+k*0=a^(2)`
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