## Question

The ellipse *x*^{2} + 4*y*^{2} = 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). Then, the equation of the ellipse is

### Solution

The given ellipse is inscribed in a rectangle *PQRS* as shown in figure. Clearly, coordinates of *P* are (2, 1). The rectangle *PQRS*is inscribed in another ellipse passing through (4, 0). So, its semi-major axis is 4.

Let the equation of the ellipse where *a* = 4.

This passes through (2, 1).

Hence, the equation of ellipse is

.

#### SIMILAR QUESTIONS

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