In the curve represented parametrically by the equations $x=2\mathrm{lncot}t+1$  and $y=\tan t+\cot t$ 
 

Tangent and normal intersect at the point (2,1)
 

Normal at $t=\frac{\pi }{4}$  is parallel to the y-axis
 

Tangent at $t=\frac{\pi }{4}$  is parallel to the line $y=x$  
 

Tangent at $t=\frac{\pi }{4}$ is parallel to the x-axis