Consider the function f : R 2 → R: f(x, y) = ax^2 + by^2 , where a and b are real constants. (a) Assume a, b > 0. Sketch a contour plot for the function f, including the level set at 1. (b) Assume a > 0 and b < 0. Sketch a contour plot, including the level set at 1. (c) Describe the level set at 1 when a = 0, b ̸= 0 and when a ̸= 0, b = 0.

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