Wua Save this response:.Detennine - whether the graph of the equation _ is symmetric with respect to = y=x2+Tx+ 10 the Xaris, the y tris eatura origin X-axis Y-axis...

Determine whether the graph of each equation is symmetric with respect to the origin. $$x^{2}+y^{2}=10$$

Yeah. Well the number 18 which is accessed square minus Y squared equal to 10. We need to check if it is symmetric about X. X. Or Y axis. So to check the cemetery about X. Access we have replaced why with minus Y in this original equation. and observe the question then. Minds wire holds quite equal to 10 which will be equal to access choir plus y squared equal to 10. Okay now this is access squared plus Y is equal to 10 Which is oh sorry access squared minus was quite equal to 10 because mine's Y squared is always Y squared which is similar to the original equation which is exactly the same. So yes it is symmetrical about the success be to check symmetry about why access we will be replacing X with mine sex in a rational equation. So minus X. Whole square minus was quite equal to 10 which means access Squire minus Y squared will be equal to 10. So this is exactly the original question. So yes. So you can say that this is. This equation is symmetrical about both X and Y axis. Thank you.

Mhm. The equation X squared equals five plus y square one test. Is this metric about the X axis? Well if it is or replace why with a negative, why? We'll get the same equation negative wise where it is the same as Y squared. That's the same as the original one. So yes it should be symmetric about the X axis. What about the Y axis? Well then that's when we replace X with negative acts. And ask ourselves. So we get the same equation will negative X squared is x squared. So we get the original equation against symmetric about the Y axis in the origin, replace X with negative acts. Why with negative? Why? And do we get the same equation for negative back squares? X squared negative. Y is squared is why squared we get the same again. It should be symmetric about all three. We graph this in the calculator decimals. We can confirm that it is symmetric about the X axis, about the Y axis and about the origin. Yeah.

We have the equation X equals a negative absolute value of Y minus four. We can test to see if it's symmetric with respect to the X axis by substituting negative Y. In for why? Which would be the negative absolute value of Y -4. Which is the same. That means it is symmetric about the X axis. We can test to see if it's measured about the Y axis by replacing negative X with X multiple everything by negative. Yeah. And this is not the same. Mhm. And we can test even so much about the origin by replacing X with negative X. And Y with negative Y. And see if we get the same. We would have X equals the absolute value of Y plus four, not the same. So just the X axis. This can be confirmed photographic of this. I'm using the that's what's crackin guys did we see that this is symmetric about the X axis.

We have the equation X equals y squared plus three. We can test to see if it's symmetric with respect to the X axis by replacing a lie with negative Y. So if we get the same equation, well negative Y squared is y square. We get the same thing. So it is symmetric about the X axis. The test to see if it's metric about the why access replace negative X with X. And then this would mean X equals negative Y squared minus three. This is not the same. So it's not symmetric about the Y axis and symmetric about the origin. We replace X with negative X and Y with negative why. And see if we get the same thing. That would be X equals negative Y squared minus three, not the same. So it should just be symmetric about the X axis. We can use the decimals graphing calculator and confirm the X equals Y squared plus three is symmetric about the X axis only.