Parametrization of the intersection of two given surfaces Find a parametrization of the intersection between the two curves $z=x^2-y^2$ and $z=x^2+xy-1$.
I figure I should set them equal to each other but I'm not sure where to go from there:
$$x^2-y^2 = x^2+xy-1$$

$$
x^2 - y^2 = x^2 + xy - 1 \\
0 = y^2 + xy - 1
$$
Apply the quadratic formula over $y$.
$$
y = \frac{x \pm \sqrt{x^2 - 4(1)(-1)}}{2(1)} = \frac{x \pm \sqrt{x^2 + 4}}{2}
$$
Alternatively, we can solve for $x$.
$$
0 = y^2 + xy - 1 \\
x = \frac{1 - y^2}{y}
$$
From there, you can continue.
