Question

Sketch the curve that satisfies the equation x^4 −4x^2 −x^2y^2 +4x^2 = 0
If you cannot give a sketch, see if you can find an argument as to why the solution curve is not the graph of a function.

Answer 1

collect like terms

\[x^4 - x^2y^2 = 0\]

then

\[x^2y^2 = x^4\]

divide both sides by x^2

\[y^2 = x^2\]

take the square root of both sides

\[y = \]

Answer 2

oops