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If Sa n dS ' are two foci of ellipse ...

If `Sa n dS '` are two foci of ellipse `16 x^2+25 y^2=400a n dP S Q` is a focal chord such that `S P=16 ,` then find `S^(prime)Qdot`

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Given ellipse is `(x^(2))/(25)+(y^(2))/(16)=1`
Here, a=5 and b=4
Now, PSQ is focal chord, where S is focus.
We know that, `(1)/(SP)+(1)/(SQ)=(2a)/(b^(2))`
Then for given ellipse, we have
`(1)/(16)+(1)/(SQ)=2xx(5)/(16)`
`rArr (1)/(16)+(1)/(SQ)=(5)/(8)`
`rArr SQ=(16)/(9)`
Now, `SQ+SQ=2a=10`
`:. SQ=10-(16)/(9)=(74)/(9)`
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