Question

1. find examples of conic sections in art and architecture. visit web sites to find pictures of artwork or buildings that illustrate one or more conic sections. in your post, give the link as well as your analysis of which conic section is used. examples already given in the lessons for this unit are off limits, so look for something new!
2. one of the biggest challenges in working with conic sections is to look at an equation in standard form and determine which section it describes. explain how you determine which conic section a particular equation describes.
3. what questions do you still have about the unit? ask them here, and your classmates may give you the answers you seek.

Explanation:

1.

Search online for art and architecture examples not covered in lessons. Analyze and provide link and conic - section identification. For example, the St. Louis Gateway Arch resembles a parabola. You can visit websites like architecture.com and search for unique buildings. If you find a building with a dome - shaped roof, it may represent a semi - circle (a part of a circle, a conic section). Provide the link to the picture and explain how it represents the conic section.

For a general second - degree equation \(Ax^{2}+Bxy + Cy^{2}+Dx + Ey+F = 0\). If \(B = 0\): If \(A = C\), it's a circle (\(x^{2}+y^{2}=r^{2}\) is a standard circle equation). If \(A
eq C\) and \(AC>0\), it's an ellipse (\(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1\) for an ellipse). If \(AC = 0\) (either \(A = 0\) or \(C = 0\)), it's a parabola (\(y=ax^{2}+bx + c\) or \(x = ay^{2}+by + c\)). If \(AC<0\), it's a hyperbola (\(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) or \(\frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1\)).

This is an open - ended part for students to ask any remaining questions about conic sections unit.

Answer:

Find a website link with a new art or architecture example and analyze the conic section used.

2.