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Algebra II Videos 107 videos
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Equations of Circles 3058 Views
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Description:
Equations of circles are a no-brainer. If aliens can do it, so can you. All you do is substitute the center of the circle's coordinates into the equation and plug in the radius. Voilà! You have your equation.
Transcript
- 00:03
Equations of circles, a la Shmoop. [title page]
- 00:06
Farmer Pete is furious about the graffiti in his corn field. [plane flies over corn field]
- 00:09
Convinced this is the work of a band of local teenagers, Farmer Pete decides to hide out
- 00:14
one night and catch them red-handed. [Pete hides]
- 00:17
Just as Farmer Pete is dozing off, a bright light in the sky begins descending toward
Full Transcript
- 00:22
the field.
- 00:23
He can't believe his eyes: aliens! [aliens arrive in field]
- 00:24
To his amazement, the aliens begin rolling out some plans, on which is written the equation
- 00:30
"(x-h)^2 + (y-k)^2 = r^2," where r is the radius and (h,k) are the coordinates of a
- 00:43
circle's center. [aliens roll out plans]
- 00:44
As farmer Pete watches, the aliens begin to march around in a circle, smashing down the
- 00:48
corn stalks. [aliens march through corn]
- 00:50
Farmer Pete, not known for his courage, decides to leave the aliens alone as long as their
- 00:55
circles are fairly small, with a radius of 2.
- 00:58
The aliens decide to park their spaceship at point (3,2), which we can consider as as
- 01:04
the circle's center. [circle's center marked]
- 01:05
The equation of a circle is (x-h)^2 + (y-k)^2 = r^2. [equation demonstrated]
- 01:13
Since point (3,2) is the circle's center, we can substitute 3 as h and 2 as k to get
- 01:20
(x-3)^2 + (y-2^2) = r^2. [substitutions made in equation]
- 01:28
Since Farmer Pete can live with circles of radius 2, we can substitute 2 in for r. (x-3)^2
- 01:36
+ (y-2)^2 = 2^2.
- 01:40
Suddenly, farmer pete has an epiphany.
- 01:43
He can take advantage of these crop circles. [Pete has an idea]
- 01:46
The A-MAZE-ing Labyrinth... here we come! [tourist attraction sign]
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