JEE Math Practice Question

Given : A circle, $$2{x^2} + 2{y^2} = 5$$ and a parabola, $${y^2} = 4\sqrt 5 x$$. Statement-1 : An equation of a common tangent to these curves is $$y = x + \sqrt 5 $$. Statement-2 : If the line, $$y = mx + {{\sqrt 5 } \over m}\left( {m \ne 0} \right)$$ is their common tangent, then $$m$$ satiesfies $${m^4} - 3{m^2} + 2 = 0$$.

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