$6. If P is a point on the ellipse \frac{x^2}{16}+\frac{y^2}{25}=1 whose foci are S and S\text{'}, then find the value of PS+PS\text{'}.$
(Answer:- PS+PS'=2a Ans. 10)

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{By} \mathrm{definition} \mathrm{of} \mathrm{ellipse}, \mathrm{we} \mathrm{know} \mathrm{that} \\ \mathrm{PS}+\mathrm{PS}\text{'}=2\times \mathrm{length} \mathrm{of} \mathrm{major} \mathrm{axis} \\ \mathrm{We} \mathrm{have} \\ \frac{{\mathrm{x}}^2}{16}+\frac{{\mathrm{y}}^2}{25}=1 \\ \frac{{\mathrm{x}}^2}{4^2}+\frac{{\mathrm{y}}^2}{5^2}=1 \\ \mathrm{Hence} \mathrm{length} \mathrm{of} \mathrm{major} \mathrm{axis}=5 \\ \Rightarrow \mathrm{PS}+\mathrm{PS}\text{'}=2\times 5=10 \end{gathered}$$

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