Statement I The equation of the directrix of the ellipse $4 x^2+y^2-8 x-4 y+4=0$ is $3 y=6-4 \sqrt{3}$

Statement II The equation of the latusrectum of the ellipse $x^2+4 y^2-4 x-8 y+4=0$ is $y=2+\sqrt{3}$

Which of the above statement(s) is (are) true?

If $S$ is the focus of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ lying on the positive $X$ - axis and $P(\theta)$ is a point on the ellipse such that $S P=1$, then $\cos \theta=$

A hyperbola having its centre at the origin is passing through the point $(5,2)$ and has transverse axis of length 8 along the $X$-axis. Then, the eccentricity of its conjugate hyperbola is

If $e_1$ is the eccentricity of the hyperbola $x=\sec \theta$, $y=\sqrt{2} \tan \theta$ and $e_2$ is the eccentricity of the hyperbola $x=\sqrt{2} \sec \theta$ and $y=\tan \theta$, then $\frac{e_2^2}{e_1^2}=$