If the system is rotated with $\theta$ (in anti-clock wise), match the curves in old system with new transferred equation,      

	Column-I		Column-II
i	$\theta =\frac{\pi }{4}, x^2-y^2=a^2$	P.	$x^2+y^2=a^2+b^2$
ii	$\theta =\frac{\pi }{4}, x^2+y^2=a^2+b^2$	Q.	$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
iii	$\theta =\frac{\pi }{2}, \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$	R.	$xy=\frac{a^2}{2}$
iv	$\theta =\frac{-\pi }{2}, \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$	S.	$\frac{y^2}{a^2}\_\frac{x^2}{b^2}=1$
		T.	$xy=\frac{-a^2}{2}$