How do I figure out whether the ICs are convex or concave?

Question: Randy Ratpack hates studying both economics and history. The more time he spends studying either subject, the less happy he is. But Randy has strictly convex preferences.

(a) Sketch an indifference curve for Randy where the two commodities are hours per week spent studying economics and hours per week spent studying history. Will the slope of an indifference curve be positive or negative?

(b) Do Randy’s indifference curves get steeper or flatter as you move from left to right along one of them?

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My attempt: Since he hates studying both economics and history and the more time he spends studying either subject, the less happy he is, his marginal utilities for economics and history are negative each. Therefore the slope of the ICs will be negative ($frac{dy}{dx}=-frac{U_x}{U_y}$). I cannot figure out whether the indifference curve is convex or concave. $frac{d^2y}{dx^2}=frac{d(-frac{U_x}{U_y})}{dx}=-frac{U_{xx}Uy-U_xU_{yx}}{U_y^2}$. How do I determine the sign of this expression. I do not know what the signs of $U_{xx}$ and $U_{yx}$ are.