# Thread: question for func with 2 variables

1. ## question for func with 2 variables

hi, i have a question

consider function f(x,y) = 1 - x^2 - y^2

sketch level curves for f(x,y) = c for c = -5,0,1

that is what i am to do....is it possible to sketch for c = 1? because when i re-arrange to get y in terms of everything i get y = sqroot ( (1-c)/3 - (2x^2)/3 )

which means if c = 1 we cant graph the solution, am i correct?

2. Originally Posted by fuzzylogic25
hi, i have a question

consider function f(x,y) = 1 - x^2 - y^2

sketch level curves for f(x,y) = c for c = -5,0,1

that is what i am to do....is it possible to sketch for c = 1? because when i re-arrange to get y in terms of everything i get y = sqroot ( (1-c)/3 - (2x^2)/3 )

which means if c = 1 we cant graph the solution, am i correct?
If
$\displaystyle f(x,y)=1~\implies~x=0~\wedge~y=0$

thus the "graph" consist of one point.

I've attached the graph of f together with the plane z = 1.

Perhaps it is possible to see that this plane is tangent to the paraboloid.

3. thanks for the help! makes sense now

also if i was to find the equation of the level curve f(x,y) = c which passes through the point (3sqrt(2),2sqrt(2)), how would i go about doing that?

4. oops never mind foujnd out how to do it