xy-2x=0
xy=2x
y=2, x does not equal zero
OR
xy-2x=0
t=theta
x=r*cos(t), -pi < t <pi
y=r*sin(t)
xy-2x=r*sin(t)*r*cos(t)-2*r*cos(t)
r*sin(t)*r*cos(t)-2*r*cos(t)=0
r*sin(t)*r*cos(t)=2*r*cos(t)
r*sin(t)*cos(t)=2*cos(t), r does not equal zero
r=sec(t)*csc(t)*(2*cos(t))
r=2*sec(t)*csc(t)*[cos(t)]
maybe this is where the computation in the book went wrong, you can see it's the same except for a factor of cos(t). Simplifying we get,
r=2*csc(t)
r=2/sin(t), r does not equal zero, -pi < t <pi
Even editors make mistakes