how do you graph z=sqrt(9-r^2cos^2(theta))?
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Carlos Guerrero García on 30 Nov 2022
I think that Carter Pennington was talking about the parametrized surface
with 0<=theta<=2pi and 0<=r<=3 (for real values of z)
In consecuence, I will plot the graph in the sentence with the followng lines:
[r,theta]=meshgrid(0:0.1:3,0:pi/60:2*pi); % In the supposed range
x=r.*cos(theta); % The classical definitons of the
y=r.*sin(theta); % polar coordinates for "x" and "y"
z=sqrt(9-r.^2.*(cos(theta)).^2); % The condition in the question
surf(x,y,z); % The graph
hold on; % and keep the focus on the figure for
surf(x,y,0.*x); % plotting the range in the XY plane
shading interp; % Optional for showing the mesh lines
axis equal % For an adequate view