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Question

If $$S$$ and $$S'$$ are the foci of the ellipse $$\cfrac { { x }^{ 2 } }{ 25 } +\cfrac { { y }^{ 2 } }{ 16 } =1$$ and if $$PSP'$$ is a focal chord with $$SP=8$$ then $$SS'=$$


A
4+SP
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B
SP1
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C
4+SP
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D
SP1
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Solution

The correct option is A $$4+S'P$$
$$SS'=2ae=2\times a\times\sqrt{1-\dfrac{b^2}{a^2}}$$

$$SS'=2\times 5\times \dfrac{3}{5}=6\dots (1)$$

As we know $$SP+S'P=2a=10$$

$$\Rightarrow S'P=10-SP=10-8=2\Rightarrow S'P=2$$

From equation (1)

$$SS'=6=4+S'P$$

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