Question

Sketch the curve

x^4 + y^4 = u
Where u is any positive constant.

We are supposed to be able to do this pretty easily from looking at the equation, but I'm not sure how, can anybody explain?

Answer 1

Initially I said Let a = x^2 and b = y^2 then sketched a circle on the axes of a and b with radius sqrt(u) but I couldn't project that onto the xy plane

Answer 2

The u is just a kind of scaling so u might as well put it as 1 in order to get the shape.

After that put x= 1 and -1, go from there.

Answer 3

Do what from there?

Answer 4

Well, if x=1, y= plus/minus 1 etc and plot.

Answer 5

etc? I don't know what you're saying

Answer 6

@estudier ?

Answer 7

Do you not know how to plot values on a graph?

Answer 8

Do you realize there is more than one way to interpolate between points?

Answer 9

Yes, I do.

Why do you think this requires any form of interpolation?

Answer 10

Because a graph is not a set of a dots.

Answer 11

You want a sketch, right.

A sketch is not a graph.

Answer 12

Sorry I should've said "Sketch the graph of the curve"

Answer 13

The curve is symmetric and continuous, smooth even.

Plot a few points and the sketch is simple (evidently it is not a rectangle)

Answer 14

The original question was about identifying the axes of symmetry of the curve, y=0 and x=0 are obvious, but there's more I can't figure out

Answer 15

(because I don't know what the function looks like)

Answer 16

Wait a minute, I will get you a picture.....

Answer 17

Thanks.

Answer 18

http://www.wolframalpha.com/input/?i=x^4+%2By^4+%3D1&x=4&y=8

Answer 19

How can I know that it is 'more rectangular' than a circle from looking at the equation?

Answer 20

Please? I seriously don't understand this. @estudier

Answer 21

:/

Answer 22

Plot some points x = 0 for example