(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

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

2. Relevant 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

3. 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.

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# Homework Help: Simplifying Ellipse equation?

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