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Consider the ellipse E=x^2/16+y^2/b^2=1 ...

Consider the ellipse `E=x^2/16+y^2/b^2=1` . PQ is a variable chord of the ellipse `E=0` and PQ subtends an angle `90^@` at the origin. And if `1/(OP)^2+1/(OQ)^2=25/144` then `b^2`=

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`1/(OP^2)+1/(OQ^2)=1/b^2+1/16`
`1/b^2+1/16=25/144`
`1/b^2=(25-9)/144=16/144`
`b^2=9`.
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