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The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). The equation of the ellipse is

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Consider the standard equation of the ellipse. Use the two points given in the question to find the value of ‘a’ and ‘b’.

Let the equation of the required ellipse be

Given that it passes through (4, 0)

It also passes through (2, 1), one of the vertex of rectangle.

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