prove that the common tangent of ellipse x^2/a^2+y^2/b^2=2x/c and x^2/b^2+y^2/a^2= -2x/c subtends a right angle at the origin

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prove that the common tangent of ellipse x^2/a^2+y^2/b^2=2x/c and x^2/b^2+y^2/a^2= -2x/c subtends a right angle at the origin

prove that the common tangent of ellipse x^2/a^2+y^2/b^2=2x/c and x^2/b^2+y^2/a^2= -2x/c subtends a right angle at the origin

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prove that the common tangent of ellipse x^2/a^2+y^2/b^2=2x/c and x^2/b^2+y^2/a^2= -2x/c subtends a right angle at the origin

prove that the common tangent of ellipse x^2/a^2+y^2/b^2=2x/c and x^2/b^2+y^2/a^2= -2x/c subtends a right angle at the origin

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