If σx is the standard deviation of the asset to be hedged, and σy is the standard deviation of...

The minimum variance hedge ratio answers the question of how much of the hedge to buy to hedge a given position. It minimizes the combined volatility of the primary and the hedge position. The minimum variance hedge ratio is given by the expression 103.10.b103.10.b. Effectively, this is the same as the beta of the primary position with respect to the hedge.

All other choices are incorrect.

Intuitive understanding of the hedge ratio: There are two standard deviations in play here: one, the standard deviation of the asset to be hedged (σx), and two, the standard deviation of the asset being used as the hedge(σy).  Now assume an extreme case where both the asset to be hedged and the asset being used as the hedge have a correlation of 1.  (That keeps the calculation simple.).  Also assume that the std dev of the asset to be hedged is 10% annually, and that of the asset being used as a hedge is say 20%.  At this point, just ignore all formulae, and think intuitively about how much of the hedge should we buy to have the same risk (in the opposite direction) as the primary position but in the opposite direction so the variation in the primary position is cancelled by opposite movements in the hedge position.  Obviously, we need to buy half because the asset being used as a hedge is twice as volatile.  In other words, we divided the volatility (std dev) of the primary position by the volatility of the asset being used as a hedge.In this question, σx is the standard deviation of the asset to be hedged, and σy is the standard deviation of the asset being used to hedge.  We will need to divide σx by σy.