to
.
The left branch corresponds to 
.
(called a conchoid)
has the line x = 2 as a vertical asymptote by showing that
.
Use this fact to help sketch the conchoid.
Solution: This is the conchoid. The branch lying to the right of the line
x = 2 corresponds
to .
The left branch corresponds to .
Going on to the analysis:
The equation 
implies that the points ( x, y) of the curve lie in the strip
.
In addition, x approaches 2 when
approaches an odd multiple of 
.
The equation 
implies that y approaches 
when
approaches an odd multiple of
.
Thus the curve has the line x = 2 as a vertical asymptote.
As for the loop, the equation 
says that y = 0 for 
.
That is, the loop is traced out for
.
by: nl