Hi, i need a little help in sketching contours.

Iv got the equation, z^2=1-4x^2-9y^2

then i make, z^2=c

which becomes, c=1-4x^2-9y^2

c-1 = -4x^2-9y^2

1-c= 4x^2+9y^2

which is an ellipse since (a does not equal to b, i.e 4 and 9 are different ), centre at the origin and domain 0 < c <= 1

But now i need to sketch the ellipse. I think i have to have it in its standard form,

x^2/a^2 - y^2/b^2 = 1

then sketch it, and use values of c, for which c is any number. But im not sure how to get it into its standard form and then sketch it

Any help would be much appreciated.

(sorry if this is in the wrong place, im very new to this)

Thanks