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If Sa n dS ' ' are the foci of the ellip...

If `Sa n dS ' '` are the foci of the ellipse `(x^2)/(25)+(y^2)/(16)=1` , and `P` is any point on it, then the range of values of `S PdotS ' P` is `9lt=f(theta)lt=16` (b) `9lt=f(theta)lt=25` `16lt=f(theta)lt=25` (d) `1lt=f(theta)lt=16`

A

`9lef(theta)le16`

B

`9lef(theta)le25`

C

`16lef(theta)le25`

D

`1lef(theta)le25`

Text Solution

Verified by Experts

Let `P( 5 cos theta, 4 sin theta)` be any point on the ellispe. Then , `SP=5+5e cos theta`
`S'P=5-5ecos theta`
`SP*S'P=25-25e^(2)cos^(2)theta)`
`=25-9cos^(2)= f(theta)`( say)
or `16lef(theta)le25`
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