What is the equation for level curves in an elliptical shape?

[wil3]

Homework Statement

Describe the shape of each level curve for the following function:

z= (5x^2+y^2)^.5-2x

Homework Equations

I would like to prove that the curves are elliptical by setting z as a constnat and algebraically putting the equation in standard for for an ellipse Ax^2+By^2=R^2

The Attempt at a Solution

After squaring both sides, I get to:

z^2+4xz=x^2+y^2

I do not know how to isolate the z on one side from there. Any suggestions? I feel like this is a really obvious algebra trick that I am forgetting.

Thank you very much for any help.

 

[hotvette]

Two suggestions:

- think of z as a number (that is arbitrary). No reason to isolate it

- Use the equation of the general conic Ax²+Bxy+Cy²+Dx+Ey+F=0