If two tangents drawn from a point \( (\alpha, \beta) \) lying on the ellipse \( 25x^{2} + 4y^{2} = 1 \) to the parabola \( y^{2} = 4x \) are such that the slope of one tangent is four times the other, then the value of \( (10\alpha + 5)^{2} + (16\beta^{2} + 50)^{2} \) equals ________________.
