The curve equations are  and .

Find intersection points.

Substitute in .

Imaginary roots are not considered, Hence .

Substitute in the curve equation .

The intersection points are  and .

The curve equation is .

Differentiate on each side  with respect to .

Power rule of derivative :.

Constant rule of derivative :.

At , slope of the tangent line is .

The point-slope form of line equation is .

Substitute and in the point slope form.

The tangent line is .

The curve equation is .

Differentiate with respect to .

Use the power rule of derivative :

At , slope of the tangent line is .

The slope point form of line equation is .

Substitute and in point slope form.

The tangent line eqaution is .

Graph:

Observe from the graph :

Both the tangents are perpendular to each other.

Hence the curve is orthogonal to each other.

The two curve equations are orthogonal to each other.