# A curve through a point

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• Feb 3rd 2011, 06:42 PM
Oiler
A curve through a point
The curve $xy(x+y-4) = k$ passes through the point $(3,3)$. Find the value of $k$. Would this be as simple as just plugging $(3,3)$ back into the equation to give the value $k$ at the point $(3,3)$ ?
• Feb 3rd 2011, 06:45 PM
pickslides
Yes.
• Feb 4th 2011, 04:53 AM
HallsofIvy
I would agree with Pickslides but that would make the answer wrong!
• Feb 4th 2011, 05:04 AM
Archie Meade
Hence, I will not agree with Pickslides!

No matter what point you choose on the curve,
placing the co-ordinates 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.