ShmoopTube

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Equations of circles, a la Shmoop. [title page]

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Farmer Pete is furious about the graffiti in his corn field. [plane flies over corn field]

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Convinced this is the work of a band of local teenagers, Farmer Pete decides to hide out

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one night and catch them red-handed. [Pete hides]

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Just as Farmer Pete is dozing off, a bright light in the sky begins descending toward

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the field.

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He can't believe his eyes: aliens! [aliens arrive in field]

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To his amazement, the aliens begin rolling out some plans, on which is written the equation

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"(x-h)^2 + (y-k)^2 = r^2," where r is the radius and (h,k) are the coordinates of a

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circle's center. [aliens roll out plans]

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As farmer Pete watches, the aliens begin to march around in a circle, smashing down the

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corn stalks. [aliens march through corn]

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Farmer Pete, not known for his courage, decides to leave the aliens alone as long as their

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circles are fairly small, with a radius of 2.

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The aliens decide to park their spaceship at point (3,2), which we can consider as as

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the circle's center. [circle's center marked]

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The equation of a circle is (x-h)^2 + (y-k)^2 = r^2. [equation demonstrated]

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Since point (3,2) is the circle's center, we can substitute 3 as h and 2 as k to get

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(x-3)^2 + (y-2^2) = r^2. [substitutions made in equation]

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Since Farmer Pete can live with circles of radius 2, we can substitute 2 in for r. (x-3)^2

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+ (y-2)^2 = 2^2.

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Suddenly, farmer pete has an epiphany.

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He can take advantage of these crop circles. [Pete has an idea]

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The A-MAZE-ing Labyrinth... here we come! [tourist attraction sign]

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