Question

Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.)

Answer 1

\[y=\frac{ x }{ 1+16kx }\]

Answer 2

\[\frac{ 1 }{ y }=\frac{ 1+16kx }{ x } = > \frac{ x }{ y }=1+16kx = > \frac{ x }{ y }-1=16kx \]\[ -\frac{ 1 }{ 16y^2 }*y'+\frac{ 1 }{ 16x^2 }=0\]

Am I doing it correctly so far?