(Steps Shown) A triangle is drawn in such a way that it has one vertex on the origin, another on the positive side of the x -axis, and the third on the part


Question: A triangle is drawn in such a way that it has one vertex on the origin, another on the positive side of the \(x\) -axis, and the third on the part of the ellipse \(4 x^{2}+9 y^{2}=36\) that is in the first quadrant. What should be the coordinates of the third point so as to make the area of the triangle as large as possible?

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