Indifference curve is a locus of different combinations of two goods which give the same level of satisfaction to the consumer.

(a) Convexity to origin: Indifference curve is convex to the origin due to the diminishing marginal rate of substitution.

(b) Downward sloping from left to right: Indifference curve slopes downward from left to right because the increase in units of good X requires a decrease in the number of units of the good Y. This is to maintain the same level of satisfaction.