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

Show that the curve is symmetrical about the x axis (without drawing the graph)

eq of the curve is : x^2 + 4y^2 = 1

also show that the curve is symmetric about the y axis

2. Relevant equations

3. The attempt at a solution

To prove that the curve was symmetric abou the x axis, i made x the subject of the equation of the curve:

x=(1-4y^2)^0.5 (can be positive or negative)

Then i used simple intuition:

let a particular value of y be "k" and the corresponding value of x be "c".

by simple calculation, we can conclude that for y=-k , x will still be equal to "c"

Can anyone guide me if this proof is enough or it lacks something, for the latter case, please provide an alternative but suitable proof.

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# Proof about symmetry (simple)

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