The curve equations are and .

Graph:

Graph the curves and :

Observe the graph:

The curve crosses itself at the point .

The curve crosses itself at the point .

and

and .

if , then .

if , the is never zero.

Therefore, is not a valid solution.

.

Apply pythagorean identity : .

.

Apply double angle identity: .

.

The slope of the tangent line is .

.

Consider .

Apply derivative on each side with respect to .

.

Consider .

Apply derivative on each side with respect to .

.

Substitute and in .

.

The slope of the tangent line is at the point.

Substitute , and .

.

The slope intercept form is .

Substitute and .

.

The tangent line equations are .

The tangent line equations are .