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## Homework Statement

Consider the surface and point given below:-

Surface: f(x,y)= 4-x

^{2}-2y

^{2}

Point: P(1,1,1)

a) Find the gradient of f.

b) Let C' be the path of steepest descent on the surface beginning at P and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane.

## Homework Equations

1) ∇f = <f

_{x}, f

_{y}>

2)

3)

## The Attempt at a Solution

a) ∇f = <f

_{x}, f

_{y}> = <-2x, -4y>

b)Descent means -∇f = <2x,4y>

Subbing in P(1,1,1)

-∇f = <2,4> ⇔ <1,2>

Unit vector for descent, u = (1/√5) <1,2>

,where <1,2> is the direction vector of the descent gradient.

I am really stuck here. I am not sure what they mean by the projection on the xy-plane. So are we moving from xyz to xy dimensions? And can I am not sure if I should use the projection formulas in this case or use derivatives to get the projection. Please help!!