# You will be creating a MASTERPIECE, a work of art of the Eiffel Tower that proudly displays conic sections. But of course, you will also need to display their equations, as well. ***I asked...

You will be creating a MASTERPIECE, a work of art of the **Eiffel Tower** that proudly displays conic sections. But of course, you will also need to display their **equations, as well**.

***I asked this question already and got a wonderful response except I neglected to indicate it had to be of the Eiffel Tower so I am posting it again hoping to get the same response.

***See previous question response here: http://www.enotes.com/homework-help/you-will-creating-masterpiece-work-art-that-469492

The level of involvement is reflected in the price I’m willing to pay for this project

Please review rubric below for guidelines

**The art work must contain:**

- At least
**10**conic sections (**2**of each conic – parabolas, circles, ellipses, and hyperbolas)-PLUS at least 4 MORE - Equations for
**ALL**conics used in your art work neatly labeled and written- - At least
**4**domain restrictions (your conic will not necessarily go on forever and forever and you will need to show where you are stopping them on your equation sheet)- - At least
**5**conics NOT CENTERED at the origin-

**Physical product of the project:**

** Technical rendering:** One piece of graph paper with your masterpiece with each conic clearly labeled by letter.

**Artistic rendering:** A second piece of paper with a copy of your drawing of the Eiffel Tower. Each conic should be outlined in black.

**Include a completed chart** with the letter corresponding to the conic section in your picture conic section, the name of the conic section, the equation of the conic section and any restrictions on the domain or range. Layout should be:

**Letter: Name of Equation: Equation in Standard For: Restrictions for each**

**Rubric:**

Chart with equations showing Letter: Name of Equation: Equation in Standard Form: Restrictions for each and are indicated on drawing

The equation representing each conic is correct

At least 4 MORE than the required numbers of conics are used

There are 4 restrictions in the domain or range

At least 5 conics are not centered at the origin

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### 1 Answer

The following figure bears a close resemblance to the Eiffel Tower. The conic sections used are:

Hyperbola

`x^2/2 - (y-8.5)^2/4 = 1`

`x^2/2.5 - (y-8.5)^2/4 = 1`

Circle

x^2 + (y-8)^2 = 3

x^2 + (y - 8)^2 = 2.5

Parabola

-0.06x^2 = = y-2

-0.06x^2 = = y-2.5

Ellipse

2x^2 + (y - 10)^2 = 4

2x^2 + (y - 10)^2 = 4.5

The restrictions for the conic sections cannot be given as a domain of x as the shape to be drawn requires the sections to extend in both directions. A closer approximation can be created by using shapes that are slanted to the axes but that would make their equations very complicated as a product of x and y has to be used in several of the terms.

The figure, and equation of the conic sections used are visible at the following link: Eiffel Tower

**Sources:**

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