Which point lies on the level curve \(f(x,y)=1\) of \(f(x,y)=x^2-y\)?

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Review the concept: Level curve

A level curve of a function \(f\) of two variables is the set of points in the plane where \(f\) takes one same constant value \(c\).

More practice problems: level curve

• ZW-LEVEL-CURVE-001 For f(x,y)=x^2+y^2, what is the level curve f(x,y)=4?
• ZW-LEVEL-CURVE-002 The level curve f(x,y)=3 of f(x,y)=2x-y is the line:
• ZW-LEVEL-CURVE-004 What is the level curve f(x,y)=0 of f(x,y)=xy?
• ZW-LEVEL-CURVE-005 For f(x,y)=x^2+y^2, for which values of c is the level curve f(x,y)=c empty?
• ZW-LEVEL-CURVE-006 Can two different level curves of the same function f intersect?
• ZW-LEVEL-CURVE-007 The level curve f(x,y)=4 of f(x,y)=x^2+4y^2 meets the x-axis at:
• ZW-LEVEL-CURVE-008 For f(x,y)=x^2+y^2, how many times larger is the radius of the level curve f=9 than that of f=1?
• ZW-LEVEL-CURVE-009 For f(x,y)=(y)/(x), the level curve f(x,y)=2 is:

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