Given: A circle, 2 x^2+2 y^2=5 and a parabola, y^2=4 √ 5 x. Statement - I: An equation of a common tangent to these curves is y=x+√ 5. Statement -…

Given : A circle, $\displaystyle 2 x^2+2 y^2=5$ and a parabola, $\displaystyle y^2=4 \sqrt{5} x$. Statement - I : An equation of a common tangent to these curves is $\displaystyle y=x+\sqrt{5}$. Statement - II : If the line, $\displaystyle y=m x+\frac{\sqrt{5}}{m}(m \neq 0)$ is their common tangent, then m satisfies $\displaystyle \mathrm{m}^4-3 \mathrm{~m}^2+2=0$.