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How is curve C(b) converted to elliptic curve?

How can we transform curve C(b): (3+b)X^2Y+(9+b)XY^2-(4+b)X^2Z+(3-b^2)XYZ+(-4+b)Y^2Z+(-9+b)XZ^2+bY*Z^2 into an elliptic curve without valuing b?

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How is curve C(b) converted to elliptic curve?

How can we transform curve C(b): (3+b)X^2Y+(9+b)XY^2-(4+b)X^2Z+(3-b^2)XYZ+(-4+b)Y^2Z+(-9+b)XZ^2+bY*Z^2 $$ C(b)\ :\ (3+b)X^2Y + (9+b)XY^2 - (4+b)X^2Z + (3-b^2)XYZ + (-4+b)Y^2Z + (-9+b)XZ^2+bYZ^2 $$ into an elliptic curve without valuing b?$b$?

Edited: Expression in code format:

(3+b)*X^2*Y + (9+b)*X*Y^2 - (4+b)*X^2*Z + (3-b^2)*X*Y*Z + (-4+b)*Y^2*Z + (-9+b)*X*Z^2 + b*Y*Z^2