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 $\cos \theta=$

If $a x^2+b y^2=15$ is the equation of the ellipse for which distance between its foci is 2 and distance between its directrices is 5 , then $a+b=$

Assertion (A) The image of $\frac{x^2}{25}+\frac{y^2}{16}=1$ in the line $x+y=10$ is $\frac{(x-10)^2}{16}+\frac{(y-10)^2}{25}=1$

Reason ( $\mathbf{R}$ ) The image of a curve ' $C$ ' in a line $L$ is the locus of the image of every point of $C$ with respect to the line $L$. The correct option among the following is :