8.2 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Circle | Obsidian::STEM | geometry::circle |
|
Overview
A circle is a shape consisting of all points in a plane at a given distance from a given point, i.e. the center. In this way, a circle is characterized by its center and radius, the distance from the center to any point of the circle. The perimeter of a circle is known as its circumference.
On the cartesian, the equation of a circle with radius r and center \langle h, k \rangle is (x - h)^2 + (y - k)^2 = r^2.
Such a circle has circumference 2\pi r and area \pi r^2. A continuous segment along the circumference of a circle is called an arc.
%%ANKI Basic A circle is characterized by what two properties? Back: Its center and its radius. Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI Basic In plain English, describe what a circle is. Back: A set of points at a given distance from some given point. Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI Basic The perimeter of a circle is known as what? Back: Its circumference. Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
What is the Cartesian equation of a circle with radius r and center \langle h, k \rangle?
Back: (x - h)^2 + (y - k)^2 = r^2
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Given indeterminates x and y, the following equation describes what shape? (x - h)^2 + (y - k)^2 = r^2$$
Back: A circle with radius r and center \langle h, k \rangle.
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Consider a circle with radius r. What does its circumference evaluate to?
Back: 2 \pi r
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Consider a circle with radius r. What is its area?
Back: \pi r^2
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Consider a circle with diameter d. What does its circumference evaluate to?
Back: \pi d
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Consider a circle with diameter d. What its area?
Back: \pi \left(\frac{d}{2}\right)^2
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Consider a circle with radius r. What does the following evaluate to? $2 \pi r$
Back: Its circumference.
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Consider a circle with radius r. What does the following evaluate to? \pi r^2$$
Back: Its area.
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
What is the Cartesian equation of the following shape?
!
Back: x^2 + y^2 = 1
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
What is the Cartesian equation of the following shape?
!
Back: (x - 2)^2 + y^2 = 4
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
What is the Cartesian equation of the following shape?
!
Back: (x + 1)^2 + (y + 1)^2 = 4
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
What is the Cartesian equation of the following shape?
!
Back: (x + 1)^2 + (y - 1)^2 = 4
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Rewrite equation x^2 + y^2 = 1 shifted left by a > 0.
Back: (x + a)^2 + y^2 = 1
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Rewrite equation x^2 + y^2 = 1 shifted up by b > 0.
Back: x^2 + (y - b)^2 = 1
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Rewrite equation x^2 + y^2 = 1 shifted right by a > 0.
Back: (x - a)^2 + y^2 = 1
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
Rewrite equation x^2 + y^2 = 1 shifted down by b > 0.
Back: x^2 + (y + b)^2 = 1
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
In what direction(s) is the unit circle shifted in the following? (x - 3)^2 + (y - 3)^2 = 1$$
Back: Right by 3 and up by 3.
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
In what direction(s) is the unit circle shifted in the following? (x + 3)^2 + (y - 3)^2 = 1$$
Back: Left by 3 and up by 3.
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI
Basic
In what direction(s) is the unit circle shifted in the following? (x - 3)^2 + (y + 3)^2 = 1$$
Back: Right by 3 and down by 3.
Reference: “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
END%%
%%ANKI Basic What term is used to describe a continuous portion of a circle? Back: An arc. Reference: Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.
END%%
Bibliography
- “Circle,” in Wikipedia, January 8, 2025, https://en.wikipedia.org/w/index.php?title=Circle.
- Ted Sundstrom and Steven Schlicker, Trigonometry, 2024.