  We construct bivariate orthogonal polynomials (OPs) on algebraic curves of
the form $y^m = \phi(x)$ in $\mathbb{R}^2$ where $m = 1, 2$ and $\phi$ is a
polynomial of arbitrary degree $d$, in terms of univariate semiclassical OPs.
We compute connection coeffeicients that relate the bivariate OPs to a
polynomial basis that is itself orthogonal and whose span contains the OPs as a
subspace. The connection matrix is shown to be banded and the connection
coefficients and Jacobi matrices for OPs of degree $0, \ldots, N$ are computed
via the Lanczos algorithm in $O(Nd^4)$ operations.
