JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
If \(S\) and \(S^{\prime}\) are the foci of the ellipse \(\frac{x^2}{18}+\frac{y^2}{9}=1\) and P be a point on the ellipse, then \(\min \left(S P . S^{\prime} \mathrm{P}\right)+\) \(\max \left(\mathrm{SP} . \mathrm{S}^{\prime} \mathrm{P}\right)\) is equal to :
- A \(3(1+\sqrt{2})\)
- B \(3(6+\sqrt{2})\)
- C 9
- D 27
Answer & Solution
Correct Answer
(D) 27
Step-by-step Solution
Detailed explanation
\(\mathrm{PS}+\mathrm{PS}^{\prime}=2 \times 3 \sqrt{2}\) \(\mathrm{b}^2=\mathrm{a}^2\left(1-\mathrm{e}^2\right) \Rightarrow 9=18\left(1-\mathrm{e}^2\right)\) \(\Rightarrow \mathrm{e}=\frac{1}{\sqrt{2}}\) Directrix…
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