
#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

Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,418

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

HW Helper
P: 3,436

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

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,900

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



Register to reply 
Related Discussions  
continuum mechanics symmetry proof  Introductory Physics Homework  0  
Special relativity: proof of symmetry concept  Introductory Physics Homework  2  
Proof of transformational symmetry  Calculus & Beyond Homework  1  
SU(3) symmetry and simple zeros of w. f.  Quantum Physics  2  
Symmetry of a circle proof  Introductory Physics Homework  8 