two variables are ever multiplied together. So squaring a variable, or multiplying two different variables, is allowed, but cubing a variable, or multiplying one variable by the square of another, is strictly forbidden. Curves in this class, including ellipses, are still called conic sections out of deference to history; but more forward-looking algebraic geometers call them quadrics.* Now there are lots of quadratic equations: any such is of the form A x2 + B xy + C y2 + D x + E y + F= 0 for some values of the six constants A, B, C, D, E, and F. (The reader who feels so inclined can check
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