Equation for y to obtain an equation that represents circle

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The equation 2x^2 + 2y^2 = 7 represents a circle, and to express y in terms of x, it needs to be rearranged. The correct approach involves solving for y, which will yield two solutions due to the circle's symmetry, indicated by the ± symbol. The discussion emphasizes the importance of considering the graph's lower portion when selecting between the positive and negative solutions for y. Understanding the relationship between x and y is crucial for accurately representing the circle's equation. Proper algebraic manipulation will lead to the desired equation for y.
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Homework Statement


The equation that is first listed is: 2x^2 + 2y^2 = 7

Homework Equations


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The Attempt at a Solution



It's redefing the bottom portion therefore I think it's y=0,-2 because that is the range?
 
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Niaboc67 said:

The Attempt at a Solution



It's redefing the bottom portion therefore I think it's y=0,-2 because that is the range?
I do not get how you think that is a solution. The solution is an equation in the form of y = f(x) such that it is represented by the graph shown (the lower portion of the circle. This is trivial.
 
Is there something known about x that you forgot to tell us ?
 
If you use some algebra to solve the circle equation for y, you should have a ##\pm## symbol in front of the x part. You want to either choose + or - based on what the plot shows.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...

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