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

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

Reply 1

mqb2766

Original post by WannaDoMaths

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.