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$$\begin{aligned} & P S \cdot P S^{\prime}=2 a=6 \sqrt{2} \\ & \frac{P S+P S^{\prime}}{2} \geq \sqrt{P S \cdot P S^{\prime}} \\ & \Rightarrow\left(P S \times P S^{\prime}\right) \max =18 \end{aligned}$$

Minima happens when $P$ lies on major axis

$$\begin{aligned} & \Rightarrow \quad P=(3 \sqrt{2}, 0) \\ & P S=(3 \sqrt{2}-3) \cdot P S^{\prime}=(3 \sqrt{2}+3) \\ & \left(P S \cdot P S^{\prime}\right) \min =9 \\ & \left(P S \cdot P S^{\prime}\right) \min +\left(P S \cdot P S^{\prime}\right) \max =27 \end{aligned}$$

Option (1)

19:T4e7,

$$\begin{aligned} & a=3 \sqrt{2}, b=3 \\ & \Rightarrow \quad e=\frac{1}{\sqrt{2}} \end{aligned}$$

JEE Main 2025 (Online) 2nd April Morning Shift Mathematics - Ellipse Question 23 Hindi Explanation

न्यूनतम तब होता है जब $P$ दीर्घ अक्ष पर स्थित हो

$$\begin{aligned} & \Rightarrow \quad P=(3 \sqrt{2}, 0) \\ & P S=(3 \sqrt{2}-3) \cdot P S^{\prime}=(3 \sqrt{2}+3) \\ & \left(P S \cdot P S^{\prime}\right) \min

Ellipse

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