We consider the differential equation $$(x^2;-;1)u_{xx};+;2xyu_{xy};+;(y^2;-;1)u_{yy};+;gxu_x;+;gyu_y;=;lambda_nu,;(*)$$ where $lambda_n;=;n(n;+;9;-;1)$. We show that the differential equation (*) has a polynomial set as solutions if $g;{ eq};-1$, -3, -5, $cdots$. Also, we construct an orthogonalizing distributional weight for g < 1 and $g;{ eq};1$, 0, -1, $cdots$ by regularizing a one-dimensional integral with a singularity on the endpoint of the interval.