The hyperbolic equation which is asymptote with hyperbola 2x ^ 2-y ^ 2 = 2 and confocal with ellipse x ^ 2 + 2Y ^ 2 = 2 is?

6x^2-3y^2=2

It is known that a point P on the hyperbola x2-y2 = A2 leads to the vertical lines PQ and PR of two asymptotes, which proves that the area of rectangular PQOR is a fixed value

Let the length of PQ and PR be a and B, then we only need to prove that PQ * pr (AB) is the fixed value. Let P (x1, Y1) ∵ asymptote be y = ± x ∥ distance formula from point to line: A and B are equal to | y ± x | / √ 2 | AB = | y ^ 2-x ^ 2 | / 2 respectively

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