Suppose that we were given a utility

function U(X1,X2)= X²,X² , What do its indifference curves look like?

The indifference curves for this utility function will be parabolas. Each indifference curve will be a parabola with its vertex at the origin and its arms extending outwards in both directions. The shape of the parabola will depend on the relative values of X1 and X2. If X1 and X2 are equal, the parabola will be symmetrical. If X1 and X2 are not equal, the parabola will be asymmetrical.