4) A headboard for a bed is built in the shape of a semielliptical arch. The headboard will be 8 feet across its base and have a height of 3 feet. Find the height of the headboard at a distance of 2 feet from its center, rounded to 3 decimal places. Clearly show your thinking, which should include a sketch of a semielliptical headboard on a set of axes and an equation that models the headboard.

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A: I am attaching image so that you understand each and every step.

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A: find intersection

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