Equation of Level Curve

[DeadxBunny]

Original question: Find an equation of the level curve of f(x,y) = yx^2 – y^2 through the point (2,1) and find an equation of the tangent line to the level curve at this point.

I think I have found the equation of the tangent line to the level curve: 10 = 4x + 2y (is this correct??), but I have no idea how to find the equation of the level curve. Please help! Thank you!!

[HallsofIvy]

You've done the hard part!

at (2,1), x= 2, y= 1 so f(x,y)= f(2,1)= 1(4)- 1= 3. The whole point of a "level" curve is that the function stays at the same "level", i.e. the same value.
The level curve is f(x,y)= yx2- y2= 3.

Yes, your tangent line is correct.