Coordinate Geometry: JEE Main 2022 Mathematics question

Let a line L₁ be tangent to the hyperbola ${{{x^2}} \over {16}} - {{{y^2}} \over 4} = 1$ and let L₂ be the line passing through the origin and perpendicular to L₁. If the locus of the point of intersection of L₁ and L₂ is ${({x^2} + {y^2})^2} = \alpha {x^2} + \beta {y^2}$, then $\alpha$ + $\beta$ is equal to _____________.