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The minimum distance of the hyperbola x^2- 4y^2=1 in the x-y plane from the variable plane x-2y+mz+2=0 where r belongs to real number is

1) dependent on m
2) infinity for at least one m
3) zero for every m
4) 2 if m=-2


It should definitely depend on m 
so the first option 1) is correct
it it can never be infinity
it cannot be zero for all m

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