A question regarding how to define a plane

[EliasR]

Today I took a math test and one of the questions was:

"Prove that 4x + 3y = 7 is a tangent plane to x² + 2xy + y = 4 and state the tangent point."

This question confused me, since the question didn't state that x or y were functions of any variables. Therefore I'm thinking that both of the equations are in fact not planes (3 dimensions), but graphs (2 dimensions).

I'm also thinking that there is no way to get a (x,y,z) point, since the functions only consist of 2 variables.

Am I thinking completely wrong or is the question incorrectly stated?

Also, my first language is not English so forgive me if I am using the wrong terms.

Thanks!

 

[tkhunny]

First, do they intersect?
Second, If so, where?
Third, Any three noncolinear points define a plane. There I no need to assume only three planes exist.