JEE Math Practice Question

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 $${m^4} + 2{m^2} = 24$$

1. A.Statement-1 is false, Statement-2 is true.
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
3. C.Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
4. D.Statement-1 is true, Statement-2 is false.