If PSQ is a focal chord of the ellipse $16 x^{2} + 25 y^{2} = 400$ such that SP = 8 then the length of SQ =

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\frac{11}{3}

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Solution

The correct option is A 2
$\frac{1}{S P} + \frac{1}{S Q} = \frac{2 a}{b^{2}}$
a= 5
b=4
Solving we get,
SQ=2.

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P S Q

16 x^{2} + 25 y^{2} = 400

S P = 8

S Q =

16 x^{2} + 25 y^{2} = 400

16 x^{2} + 25 y^{2} = 400.

16 x^{2} + 25 y^{2} = 400.

PSQ is a focal chord of the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{9}$ = 1 then $\frac{1}{S P} + \frac{1}{S Q}$ =

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