Problems from Definitions, matrix and main matrix of the conics

Consider the matrix A=[212110203] What is the analytical equation of the conic associated with the previous matrix?

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Development:

We know that the conic defined by the matrix A is given by the equation (x,y,1)A(x,y,1)T=0. Therefore, [xy1][212110203][xy1]=[xy1][2x+y+2x+y2x+3]= =2x2+xy+2x+xy+y2+2x+3=2x2+y2+2xy+4x+3

Solution:

The analytical equation of the conic is q(x,y)=2x2+y2+2xy+4x+3

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