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Proof about symmetry (simple) 
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#1
Dec2311, 01:58 AM

P: 247

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=(14y^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. 


#2
Dec2311, 10:28 AM

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P: 7,819

For symmetry w,r,t, the yaxis, replace x with x, in the original, and check to see that the result is equivalent to the original. 


#3
Dec2311, 10:34 AM

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P: 3,562

It is enough proof to show that f(x)=f(x) for symmetry about the yaxis, and f(y)=f(y) for symmetry about the xaxis. Can you see why?
Basically, this just means you just need to show that the function doesn't change when you swap x for x and y for y. edit: If I bothered to refresh the page to see if a reply was already made, we wouldn't be here right now... 


#4
Dec2311, 02:06 PM

P: 247

Proof about symmetry (simple)
alright, from your replies i think the method i used is correct.
So thnx guys ! cheers 


#5
Dec2411, 06:50 AM

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Thanks
PF Gold
P: 39,682

Yes, correct, but do you understand that everyone was telling you that you don't have to solve for one variable?



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