(x^(2))/(9)+(y^(2))/(16)+(x^(2))/(9)=1

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15x^(2)-4y^(2)+15z^(2)=-4

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

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

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4x^(2)-4y+z^(2)=0

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4x^(2)-y^(2)+4z=0

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y^(2)+z^(2)=9

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y^(2)+z=6

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4x^(2)+y^(2)=4

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y^(2)-z^(2)=25

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4x^(2)-y^(2)-z^(2)=1

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(x^(2))/(16)+(y^(2))/(25)+(x^(2))/(25)=1

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16x^(2)-y^(2)+16z^(2)=4

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

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x^(2)+(y^(2))/(4)+z^(2)=1

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z^(2)-x^(2)-(y^(2))/(4)=1

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z^(2)=x^(2)+(y^(2))/(9)

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3z=-y^(2)+x^(2)

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x^(2)-y^(2)+z=0

MTH 252 Project Due: November 30, 2023 Introduction. This project requires you to use computer programs to plot equations of surfaces (mostly quadric surfaces) in the space. The project is two-fold: On the one hand, it gives you an opportunity of applying technology for the study of Calculus. On the other hand, by plotting the surfaces in a 3-dimensional space, you gain insights about some basic quadric surfaces, about which you may ask further questions, such as whether they are bounded or not, what are their tangent planes at a point, and questions related to minimum, maximum, or the nature of critical points. Method. You may work alone or in a group of up to 3 people, following the rules below: - Type all the names in your group in your project. - You can use any convenient graphing software such as Mathematica, Maple, Matlab, SAGE, etc. - You need to include the codes (commands) in your work. - The output should be 3-d graphing of the equations given in the problems. - For each output (graph), you should describe the figure by its name, such as ellipsoid, paraboloid, etc. - Pending on your professor, a group of size n(1n3) will get 2n equations for your project (that is, you will complete the plotting of 2 equations by yourself (if you are working alone), or 2n equations within your group of size n=2 or n=3 ). Important: Please do not to copy work from other groups (such as using identical typing and identical codes). If that happens, both groups will have a very low grade. Unless the project descriptions are not clear, the ideal situation is that do not ask your professor how to complete the project. Figure out an answer by yourself or within your group. (Hint: You may read the text, or google to get more information.) 1. 9x2+16y2+9z2=1 2. 15x24y2+15z2=4 3. 4x2y2+4z2=4 4. y2=4x2+9z2 5. 4x24y+z2=0 6. 4x2y2+4z=0 7. y2+z2=9 8. y2+z=6 9. 4x2+y2=4 10. y2z2=25 11. 4x2y2z2=1 12. 16x2+25y2+25z2=1 13. 16x2y2+16z2=4 14. z=x2+4y2 15. x2+4y2+z2=1 16. z2x24y2=1 17. z2=x2+9y2 18. 3z=y2+x2 19. x2y2+z=0