Find the condition that the curves 2x = y2 and 2xy = k intersect orthogonally.

It’s seen that the given bends are condition of two circles.

   

and

   

We realize that, two circles converge symmetrically if the point between the digressions attracted to the two circles at the place of their convergence is 90o.

Presently, separating conditions (1) and (2) w.r.t. t, we get

Presently, settling conditions (1) and (2), we have

   

Placing the worth of y in condition (1),

   

   

   

   

Subsequently, the necessary condition is