Stitz-Zeager_College_Algebra_e-book

The vertices of a hyperbola are the points of the

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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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