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Consider the equation y4 = 3(32 — y2), where a is a real number

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Consider the equation y4 = 3(32 — y2), where a is a real number. This is the equation of a curve that can look quite different depending on the value of a. You are encouraged to play with it a bit using your preferred graphing software. (a) For what values of a are there are points on the curve at which the tangent lines are horizontal? State the answer as a set, and carefully explain why it is correct. (b) For all values of a in the set you answered above, ?nd the coordinates (both coordinates) of all points on the curve at which the tangent lines are horizontal. Your answer(s) should be in terms of a, and explained well.