Determine whether each equation has a graph that is symmetric wit...

Question

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. 
5y^2 + 5x^2 =30

Accepted Answer

Welcome back. I am so glad you're here. We are asked to identify if the graph defined by the following equation is symmetric with respect to the origin, the X axis, the Y axis or none. So the equation that we're given is eight Y squared plus eight X squared equals 56. Now we recall from previous lessons that when we're checking for symmetry, I'm going to start with the X axis. When we're checking for symmetry with regards to the x axis, what we're going to do is we're going to plug a negative Y in for why. And we're going to see if we get the same equation back. So it'll be eight times no longer Y squared. It'll be a negative Y still squared plus eight X squared equals 56. And so we do the work here, negative Y squared will negative Y squared equals Y squared. So this brings us back to eight Y squared plus eight X squared equals 56. Now, if we get the same equation that we started with, then it is symmetric with respect to the X axis. And we do have the same equation that we started with So it is symmetric with respect to the X axis. Alright, now let's test the Y axis for testing the Y axis. We are going to put a negative X in for X and see if we get the same formula back or equation back. Excuse me. So we have eight Y squared plus eight times not X squared, but now a negative X Still squared equals 56. And now we do that simplification. So we have eight Y squared plus eight times negative X squared equals X squared that equals 56. And we ask ourselves, did we get the original equation back again? Yes, we did. It is the same. So we do have symmetry with respect to both the X axis and the Y axis. And when we have symmetry with respect to both the X axis and the Y axis, or in other words, we put negative Y in for Y and get the same thing back. We put negative X in for X and get the same thing back. Then we have respect to the origin. So we have symmetry with respect to all three. We look at our answer choices and that's answer choice. C the graph is symmetric with respect to the x axis, Y axis and the origin. Well done. We'll catch you on the next one.

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. 5y^2 + 5x^2 =30

Key Concepts

Symmetry in Graphs

Identifying Symmetry

Conic Sections

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