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If P (x,y) be any point on 16x^(2) +...

If P (x,y) be any point on ` 16x^(2) + 25y^(2) = 400` with foci ` F_(1) (3,0) and F_(2) (-3,0)` then ` PF_(1) + PF_(2)` is

Text Solution

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We have, ellipse
`16x^(2)+25y^(2)=400`
or `(x^(2))/(25)+(y^(2))/(16)=1`
`:. a^(2)e^(2)=a^(2)-b^(2)=25-9`
`:. ae=3`
So, foci, are `(+-ae,0) -=(+-3,0)`
Since `F_(1) and F_(2)` are the foci of the ellipse.
Since the sum of the focal distances of a variable point P on an ellipse is equal to its major axis,
`PF_(1)+PF_(2)=2a=10`
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