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If the normal at P(2,(3sqrt(3))/2) meets...

If the normal at `P(2,(3sqrt(3))/2)` meets the major axis of ellipse `(x^2)/(16)+(y^2)/9=1` at `Q` , and `S` and `S '` are the foci of the given ellipse, then find the ratio `S Q : S^(prime)Qdot`

Text Solution

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Equatio of ellipse `P(2,(3sqrt(3))/(2))`
`:. e^(2)=1-(9)/(16)+(7)/(16)`
`rArre=(sqrt(7))/(4)`
Hence , foci are `S(sqrt7,0) and S(-sqrt(7))`

Normal at P bisects the angle `angleSPS''`
Therefore, in triangle SPS' using bisector theorem, we get `(SQ)/(S'Q)=(SP)/(S'P)=(a-ex)/(a+ex)=(4-(sqrt(7))/(4)xx2)/(4+(sqrt(7))/(4)xx2)=(8-sqrt(7))/(8-sqrt(7))`
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