EllipseHard

Question

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

Options

A.x2 + 16y2 = 16
B.x2 + 12y2 = 16
C.4x2 + 48y2 = 48
D.4x2 + 64y2 = 48

Solution

         
x2 + 4y2 = 4 ⇒ = 1 ⇒ a = 2, b = 1 ⇒ P = (2, 1)
Required Ellipse is
(2, 1) lies on it
⇒    
∴     = 1 ⇒ x2 + 12y2 = 16

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