Question

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

Answer 1

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