maya_jai_singh
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hey, sorry to disturb anyone.

I was just wondering how to sketch the graph of ((y^2)-2)^2 + ((x^2)-2)^2 = 2.

I've found turning points and discovered asymptotes at x=0 and y=0 and also discovered the graph exists in all 4 quadrants. I get that the graph looks similar to that of a circle but I sketched it in Desmos and am clueless to why it has the shape it does.

Some help would be greatly appreciated!
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DFranklin
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Do you understand why (|y|-2)^2+(|x|-2)^2 = 2 has the shape it does?

Also, where is this from? Because I'm sure there's been a discussion about this graph before.
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RDKGames
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(Original post by maya_jai_singh)
hey, sorry to disturb anyone.

I was just wondering how to sketch the graph of ((y^2)-2)^2 + ((x^2)-2)^2 = 2.

I've found turning points and discovered asymptotes at x=0 and y=0 and also discovered the graph exists in all 4 quadrants. I get that the graph looks similar to that of a circle but I sketched it in Desmos and am clueless to why it has the shape it does.

Some help would be greatly appreciated!
The fact that x^2,y^2 make an appearance (and nothing else does) means the graph has not only symmetry in the y-axis, but also the x-axis.

This is why you see it symmetrically in all four quadrants.

The shapes themselves are then slightly weird, but this is simply due to the nonlinearly of what's inside the squared brackets. You should expect a closed shape since this is very nearly a circle.
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maya_jai_singh
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(Original post by DFranklin)
Do you understand why (|y|-2)^2+(|x|-2)^2 = 2 has the shape it does?

Also, where is this from? Because I'm sure there's been a discussion about this graph before.
Yeah, so would the graph you've mentioned just be the graph of (y-2)^2 + (x-2)^2 but in all 4 quadrants?

I'm doing a set of 99 interview questions, this is one of the questions from there.
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maya_jai_singh
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(Original post by RDKGames)
The fact that x^2,y^2 make an appearance (and nothing else does) means the graph has not only symmetry in the y-axis, but also the x-axis.

This is why you see it symmetrically in all four quadrants.

The shapes themselves are then slightly weird, but this is simply due to the nonlinearly of what's inside the squared brackets. You should expect a closed shape since this is very nearly a circle.
Oh ok yes that makes sense.

Thanks, I was just unsure of the shape in general and how to sketch it, but this makes sense. Thank you so much once again!
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