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Find constants so two ellipses enclose equal areas

Let A, B be positive numbers with A > B. Find values of A and B such that the area of the region enclosed by the ellipse

    \[ Ax^2 + By^2 = 3 \]

is the same as the area bounded by the ellipse

    \[ (A+B)x^2 + (A-B)y^2 = 3. \]


Incomplete.

2 comments

    • Ranjan says:

      this simplifies to A=ϕB, where ϕ is the golden ratio. This can be deduced by dividing the equation by B^2

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