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If P(x ,y) is any point on the ellips...

If `P(x ,y)` is any point on the ellipse `16 x^2+25 y^2=400` and `f_1=(3,0)F_2=(-3,0)` , then find the value of `P F_1+P F_2dot`

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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