Statement 1 : An equation of a common tangent to the parabola $y^2 = 16 \sqrt{3}x$ and the ellipse $2x^2 + y^2 = 4$ is $y = 2x + 2\sqrt{3}$. <br> Statement 2 : If the line $y = mx + \frac{4 \sqrt{3}}{m}, (m \neq 0)$ is a common tangent to the parabola $y^2 = 16 \sqrt{3}x $ and the ellipse $2x^2 + y^2 = 4$, then $m$ satisfies $m^2 + 2m^2 = 24$.

Question

( A ) Statement 1 is false, statement 2 is true
( B ) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
( C ) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
( D ) Statement 1 is true, statement 2 is false