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###### Graphing x^2a + y^2b = 100

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3 weeks ago

I've got some graph sketching questions to do around functions with x and y raised to different powers and I'm not sure how to approach them? First one asks me to sketch x^4 + y^4 = 100, then x^100 + y^100 = 100 and then x^2 + y^4 = 100. I know to get the points of intersection with the axes and that the graphs are going to look circle-y but I'm not sure where to go from there to get the shape of the curve in each quadrant. Can anyone help? Thanks

Original post by WannaDoMaths

I've got some graph sketching questions to do around functions with x and y raised to different powers and I'm not sure how to approach them? First one asks me to sketch x^4 + y^4 = 100, then x^100 + y^100 = 100 and then x^2 + y^4 = 100. I know to get the points of intersection with the axes and that the graphs are going to look circle-y but I'm not sure where to go from there to get the shape of the curve in each quadrant. Can anyone help? Thanks

To understand it, it may be better to consider

x^4 + y^4 = 100^2

say, so keep the axis crossing points the same for different powers (+/-10), then (7,7) would line on a circle (approximately), but when x=7 here so 7^4~2500, then y must be >9 so ... Similary what would be the point which lay on the curve such that x=y, ...

As usual, sticking a few points in and thinking about whats going on may give enough intuition to sketch it.

Edit - a slightly more rigorous way to do it would be to do a series expansion of

(1 - x^(2n))^(1/2n)

to get the local behaviour of y (the 100 is simply replaced by 1 to normalize the axis cutting points) for small x.

(edited 3 weeks ago)

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