Number 5). Solve using mat lab Draw the surface x^2 + 16y^2 + 4z^2 = 16 by param

Question

Number 5). Solve using mat lab Draw the surface x^2 + 16y^2 + 4z^2 = 16 by parameterizing it. And also on the same graph plot the normal vectors (gradient vectors). You must label all the axes and graph should have a title that includes your name. Publish your output to HTML Develop the M file by parameterizing the given surface and use the parameterization to plot the Surface, 9x^2 - 4y^2 = 36, Also label all axes and graphs should have a title that includes your name. Publish your output to HTML.

Explanation / Answer

Matlab Executable code:

[x,y,z] = ellipsoid(0,0,0,4,1,2,40); % copy this code into ur command window and publish it
% center are (xc,yc,zc) and semi-axis lengths are (xr,yr,zr).
surfl(x,y,z) %ploting (x^2)/16+(y^2)/1+(z^2)/4=1;
% so xr=sqrt(16)=4 yr=1;zr=4;

colormap copper
grid on
rotate3d
axis equal
axis([-4 4 -1 1 -2,2]) % x=[-4 4] y=[-1 1] z=[-2 2]
view([158,14])
set(gca,'Color','y')
set(gca,'XTick',-4:1:4,'XMinorTick','on','FontName','times','FontWeight','bold')
set(gca,'YTick',-1:1:1,'YMinorTick','on','FontName','times','FontWeight','bold')
set(gca,'ZTick',-2:0.5:2,'ZMinorTick','on','FontName','times','FontWeight','bold')
title('An Ellipsoid 4x^2 + y^2 + 8z^2 = 16 (generated by the Ellipsoid Command)')
xlabel('X-Axis','Color','black','FontName','mathematica','FontWeight','bold','FontSize',12)
ylabel('Y-Axis','Color','black','FontName','mathematica','FontWeight','bold','FontSize',12)
zlabel('Z-Axis','Color','black','FontName','mathematica','FontWeight','bold','FontSize',12)

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