Ellipse

STATEMENT-1 : An equation of a common tangent to the parabola ${y^2} = 16\sqrt 3 x$ and the ellipse $2{x^2} + {y^2} = 4$ is $y = 2x + 2\sqrt 3$ STATEMENT-2 :If line $y = mx + {{4\sqrt 3 } \over m},\left( {m \ne 0} \right)$ is a common tangent to the parabola ${y^2} = 16\sqrt {3x}$and the ellipse $2{x^2} + {y^2} = 4$, then $m$ satisfies ${m^4} + 2{m^2} = 24$