68 



ON THE EQUATION OF CURVES, ETC. 



Hence, when the axis of x is parallel to an asymptote, 

 equation (1) becomes 



A/ + 2Bxy + ^T>y + 2EiP+ F=o (f). 



Similarly, when the axis of y is parallel to an asymptote, the 

 equation takes the form 



^Bxy+Cx" +2Dy + 2Ea; + F=o (g), 



and when both the axes are parallel to the asymptotes, the 

 equation becomes 



2 Ba;y + 2 Dy + 2 I> + F=o (h). 



