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If the curve C in the xy plane has the equation `x^(2)+xy+y^(2)=1,` then the fourth power of the gretest distance of a point on C from the origin is `"_____."`

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Verified by Experts

The correct Answer is:
4
Let `x=rcostheta,y=rsintheta`
`:.r^(2)(1+costheta,sintheta)=1`
or `r^(2)=2/(2+sin2theta)` or `r_(max)^(2)=2`
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