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
B
SP1
C
4+SP
D
SP1

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

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