contour plots for multiple functions

Ok so i'm completely stuck on how to do this question i've been set for uni after just one very confusing and poorly delivered lecture...

Sketch Contours for the following functions, specifying the range of values allowed for z.

a) z^2 = [f(x,y)]^2 = 9 - 4x^2 - 4y^2

b) z^2 = [f(x,y)]^2 = 1 - 4x^2 - 9y^2

c) z^2 = [f(x,y)]^2 = 1 + 9x^2 - y^2


Any help or guidance on how to even get started on these would be fantastic! Thank you

Quote:

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Originally Posted by rudders

Ok so i'm completely stuck on how to do this question i've been set for uni after just one very confusing and poorly delivered lecture...

Sketch Contours for the following functions, specifying the range of values allowed for z.

a) z^2 = [f(x,y)]^2 = 9 - 4x^2 - 4y^2

b) z^2 = [f(x,y)]^2 = 1 - 4x^2 - 9y^2

c) z^2 = [f(x,y)]^2 = 1 + 9x^2 - y^2


Any help or guidance on how to even get started on these would be fantastic! Thank you

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a) z^2 = [f(x,y)]^2 = 9 - 4x^2 - 4y^2

z^2 = 9 - 4 (x^2 + y^2)

If I understand the question correctly:

Note that x^2 + y^2 will be greater than or equal to zero, which makes -4 (x^2 + y^2) less than or equal to zero, which makes 9 - 4(x^2+y^2) less than or equal to 9.
If z^2 is less than or equal to 9, then z could be between -3 and 3.

Good luck!