Name the conic

You will write a function that names the conic given by the six numbers of $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$, and a function that finds the $y$-intercept of a tangent of a given slope. The checker uses the examples of the lesson.

The idea. Work out $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2$. If $\Delta = 0$ the equation is degenerate. Otherwise the sign of $h^2 - ab$ names the curve: negative for an ellipse (a circle if $a = b$ and $h = 0$), zero for a parabola, positive for a hyperbola (rectangular if $a + b = 0$).

Your tasks.

1. Finish classify(a, h, b, g, f, c). Return one of the words "circle", "ellipse", "parabola", "hyperbola", "rectangular hyperbola" or "degenerate".
2. Finish tangent_c(kind, a, b, m). For kind = "ellipse" use $c^2 = a^2m^2 + b^2$ and for kind = "hyperbola" use $c^2 = a^2m^2 - b^2$. Return the positive $c$, or None if the number under the root is negative.