"Find the orthogonal trajectories of the family of curves .

I know the steps: 1) solve for c...okay....
2)Find y', and plug the c back into it.
3) set dy/dx equal to the negative reciprocal of y' from pt. 2, and solve for y. This is the family of orth. traj.

My problem is finding y' for part 2. Well, I can find y', but getting it into a form so that I can solve for y in part 3.



y'=

Where should I go from here? Thanks!

Have you been taught implicit differentiation:

.

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