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Question
If P is a point on the ellipse `x^2/16 + y^2/25` = 1 whose foci are S and S′, then PS + PS′ = 8.
Options
True
False
Solution
This statement is False.
Explanation:
Let P(x1, y1) be a point on the ellipse.
Foci = (± ae, 0)
Here a2 = 25 ⇒ a = 5
b2 = 16 ⇒ b = 4
b2 = a2 (1 – e2)
16 = 25(1 – e2)
⇒ `16/25 = 1- e^2`
⇒ e2 = `1 - 16/25`
⇒ e2 = `9/25`
∴ e = `3/5`
∴ ae = `5 xx 3/5` = 3
So, the foci are S(3, 0) and S(– 3, 0).
Since PS + PS' = 2a = 2 × 5 = 10.
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