In this question, we seek to determine the area of a rectangular domain, R, with base on the x-axis and inscribed between the curve C:y-3 x and the circle of radius 3 centred in the origin, S:x²+ y²-9, and solve an optimisation problem related to it. The domain lies in the first quadrant. Let a be the x- coordinate of the top-left vertex of R and b the x-coordinate of the top-right vertex. a) By considering a line parallel to the x-axis and the vertices of R, or otherwise, find an equation relating the square of a and the square of b. We have that b^2=

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