Let the curve pass through four points
, , , ,
Find the coefficients , , , .
Solution : Substitute the coordinates of the four points into the curve equation to obtain a system of linear equations
,
Its coefficient determinant
is the transpose of a Vandermonde determinant . According to the properties of the determinant , we can get
.
and
In the same way, we can get:
;
;
.
Therefore, according to Clem's rule , we get the only solution
, , , ,
That is, the curve equation is
.
