How to find the rank and determinant of following system of equations:
$$ c_{11}x_1^2+c_{12}x_2^2 + c_{13}x_1x_2+ c_{14}x_1+c_{15}x_2= C_1$$ $$ c_{21}x_1^2+c_{22}x_2^2 + c_{23}x_1x_2+ c_{24}x_1+c_{25}x_2= C_2$$ $$ c_{31}x_1^2+c_{32}x_2^2 + c_{33}x_1x_2+ c_{34}x_1+c_{35}x_2= C_3$$
I need to find the Determinant and rank of the matrix $(x_{ij})$. Please help