Ellipse eccentricity?

Geometry Level 4

If the line 2px+y1p2=12px+y\sqrt{1-p^{2}}=1 always touches the ellipse x2a2+y2b2=1\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1  p(1,1){0}\forall \ p \in (-1,1) - \{0\}, find the eccentricity of this ellipse.

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