The equation is .

.

Differentiate on each side with respect to .

.

Find orthogonal trajectory :

Orthogonal family has negative reciprocal slope.

.

Apply cross multiplication.

.

Integrate on each side.

.

Integrate power rule:.

.

Graph the two families.

Graph the function for several values of .

Graph the orthogonal function for several values of .

Graph :

Observe the graph:

are ellipses.

are curves.

Graphs will vary.

Graph :

are ellipses.

are curves.

Graphs will vary.