
A curve through a point
The curve $\displaystyle xy(x+y4) = k$ passes through the point $\displaystyle (3,3)$. Find the value of $\displaystyle k$. Would this be as simple as just plugging $\displaystyle (3,3)$ back into the equation to give the value $\displaystyle k$ at the point $\displaystyle (3,3)$ ?


I would agree with Pickslides but that would make the answer wrong!

Hence, I will not agree with Pickslides!
No matter what point you choose on the curve,
placing the coordinates of the point into the equation
must always give the same value of k.
Hence, given the point (3,3) is on the curve,
it will yield the same constant k that any other point on the curve will yield.