Question

what questions do you have?

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.

Explanation:

1. For the first part, search on art - related and architecture - related websites like Pinterest, Artnet, and ArchDaily. Look for artworks or buildings with shapes such as circles (e.g., the Pantheon in Rome is circular, a type of conic section), parabolas (some modern architectural roofs may have parabolic shapes), ellipses (certain art installations or building facades), and hyperbolas (some cooling towers have hyperbolic shapes). Provide the website link and clearly state which conic section the shape represents.
2. For the second part, recall the standard forms of conic - section equations. If the equation is of the form $(x - h)^2+(y - k)^2=r^2$, it represents a circle. If it is of the form $\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1$ ($a

eq b$), it is an ellipse. If it is of the form $\frac{(x - h)^2}{a^2}-\frac{(y - k)^2}{b^2}=1$ or $\frac{(y - k)^2}{a^2}-\frac{(x - h)^2}{b^2}=1$, it is a hyperbola. And if it is of the form $(x - h)^2 = 4p(y - k)$ or $(y - k)^2=4p(x - h)$, it is a parabola. Analyze the coefficients and the signs of the squared terms in the given equation to determine the conic section.

Answer:

1. Search art and architecture websites for conic - section examples, provide link and analysis.
2. Analyze coefficients and signs of squared terms in standard - form equations to determine conic section.