Orthogonal Trajectories/Examples/Circles Tangent to Y Axis

Theorem
Consider the one-parameter family of curves:
 * $(1): \quad x^2 + y^2 = 2 c x$

which describes the loci of circles tangent to the $y$-axis at the origin.

Its family of orthogonal trajectories is given by the equation:
 * $x^2 + y^2 = 2 c y$

which describes the loci of circles tangent to the $x$-axis at the origin.


 * CirclesTangentAxisOrthogonalTrajectories.png