# Projection of intersection line

## Homework Statement

Find the projection of the intersection between the two surfaces

S1: z = 4-x^2 - y^2 and
S2: 4x^2y = 1 (x>0)

in the xy-plane

2. The attempt at a solution

4-x^2 - y^2 = 4x^2y -1

Is this all I need to do?

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Hurkyl
Staff Emeritus
Gold Member
Is this all I need to do?
What is it that you did?

Equalised the equations, with z = 0.

Hurkyl
Staff Emeritus
Gold Member
Equaled the equations, with z = 0.
(You can't set two equations equal... but I think I know what you meant)
(And you were looking for a geometric object, not an equation... but I assume you meant to say the object described by that equation)

Does that process have anything to do with finding the intersection of the two surfaces? Or with projecting that intersection to the x-y plane? If so, then you're done. If not, then you're not.

The problem is:

How steep is the path C (the intersection between the curves) at the point S over the (1, 1/4)?

My plan is to find the directional derivative in the direction of the tangent of the projection of C in the xy-plane. What do I do next then?

HallsofIvy