Ellipse eccentricity??

Geometry Level 4

If the line $$2px+y\sqrt{1-p^{2}}=1$$ always touches the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ $$\forall$$ p$$\epsilon$$ (-1,1) - {0} ,then find the eccentricity of ellipse.

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