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An ellipse has point (1,-1)a n d(2,-1) a...

An ellipse has point `(1,-1)a n d(2,-1)` as its foci and `x+y-5=0` as one of its tangents. Then the point where this line touches the ellipse is `((32)/9,(22)/9)` (b) `((23)/9,2/9)` `((34)/9,(11)/9)` (d) none of these

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Image of focus S(2,-1) in the tangennt at P in the tangent at P is lies on the line S'P
Let image `S'''-=(h,k)`
`:. (h-2)/(1)=(k+1)/(1)=(2(2-2-5))/(2)=4`
`rArr S'''=(6,3)`
Equation of line SS'' is
4x-5y=9
Soving tangent and SS'' , we get `P-=((34)/(9),(11)/(9))`
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