Question

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). Then the equation of the ellipse is
(a) x² + 12y² = 16 

(b) 4x² + 48y² = 48

(c) 4x² + 64y² = 48 

(d) x² + 16y² = 16

Answer 1

(a) : The given ellipse is x2/4 + y2/1 = 1 i.e., the point A, the corner of the rectangle in 1st quadrant, is (2, 1). Again the ellipse circumscribing the rectangle passess through the point (4, 0), so its equation is