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Let a line L(1) be tangent to the hyperb...

Let a line `L_(1)` be tangent to the hyperbola `(x^(2))/16 - (y^(2))/4 = 1 and " let " L_(2)` bee the line passing through the origin and perpendicular to `L_(1)`. If the locus of the point of intersection of `L_(1) and L_(2) " is " (x^(2)+y^(2))^(2) = alphax^(2) +betay^(2) , " then " alpha +beta ` is equal to _______.

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