In the above diagram, A is a circle with radius $2$ centered at the origin and B is an ellipse with major axis $4$ and minor axis $2$ centered at $(7, 5).$ If B is stretched and translated to obtain A, which of the following processes should be applied?

(i) Translate B by $-7$ and $-5$ in the positive directions of the $x$-axis and $y$-axis, respectively, and stretch by a factor of $2$ with respect to the $y$-axis.

(ii) Translate B by $-7$ and $-5$ in the positive directions of the $x$-axis and $y$-axis, respectively, and stretch by a factor of $2$ with respect to the $x$-axis.

(iii) Translate B by $7$ and $5$ in the positive directions of the $x$-axis and $y$-axis, respectively, and stretch by a factor of $\frac{1}{2}$ with respect to the $y$-axis.

(iv) Translate B by $-7$ and $-5$ in the positive directions of the $x$-axis and $y$-axis, respectively, and stretch by a factor of $\frac{1}{2}$ with respect to the $x$-axis.