Unformatted text preview:
10
2 10
, our answer becomes
4 x− 1
2 2 + y− 7
2 2 = 10
4 7.2 Circles 403 We close this section with the most important1 circle in all of mathematics: the Unit Circle.
Definition 7.2. The Unit Circle is the circle centered at (0, 0) with a radius of 1. The standard
equation of the Unit Circle is x2 + y 2 = 1.
√ 3
.
Example 7.2.5. Find the points on the unit circle with y coordinate
2
√
3
Solution. We replace y with
in the equation x2 + y 2 = 1 to get
2
x2 + y 2 = 1
√2
3
2+
=1
x
2
3
+ x2 = 1
4
1
x2 =
4
x=±
x=±
Our ﬁnal answers are 1 √
13
,
22 and √
13
−,
.
22 While this may seem like an opinion, it is indeed a fact. 1
2 1
4 404 Hooked on Conics 7.2.1 Exercises 1. Find the standard equation of the circle given the center and radius and sketch its graph.
√
(a) Center (−1, −5), radius 10
(d) Center (π, e2 ), radius 3 91
(b) Center (4, −2), radius 3
(e) Center (5, −9), radius ln(8)
√
7
1
(c) Center −3, 13 , radius 2
(f) Center −e, 2 , radius π
2. Complete the square in order to put the equation into standard form. Identify th...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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