Can you help me prove if true or false please:

True or False? Every system of two conic equations whose xy-term is nonexistent has at most 4 points of intersection. graph is not a proof.

Thanks!

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- May 12th 2010, 12:35 AMAnemoriConic Equation
Can you help me prove if true or false please:

True or False? Every system of two conic equations whose xy-term is nonexistent has at most 4 points of intersection. graph is not a proof.

Thanks! - May 12th 2010, 08:32 AMSoroban
Hello, Anemori!

I have a rather sloppy proof . . .

Quote:

True or False?

Every system of two conic equations whose xy-term is nonexistent

has at most 4 points of intersection. . . True!

We have two conic equations: .

Solve [1] for

. . Quadratic Formula: .

Substitute into [2]:

. . .

This simplifies to ain . . . which has at most 4 roots.*quartic*