Stitz-Zeager_College_Algebra_e-book

What resultant force is applied to the keg 10

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Unformatted text preview: − y sin 3 = 2 − 2 and y = x sin 3 + y cos 3 = 2 + y 2 11.6 Hooked on Conics Again 829 and simplify. While this is by no means a trivial task, it is nothing more than a hefty dose of Beginning Algebra. We will not go through the entire computation, but rather, the reader should take the time to do it. Start by verifying that √ (x )2 x y 3 3(y )2 x= − + , 4 2 4 √ √ √ (x )2 3 x y (y )2 3 3(x )2 x y 3 (y )2 2 xy = − − , y= + + 4 2 4 4 2 4 √ To our surprise and delight, the equation 21x2 + 10xy 3 + 31y 2 = 144 in xy -coordinates 2 2 reduces to 36(x )2 + 16(y )2 = 144, or (x4) + (y9) = 1 in x y -coordinates. The latter is an ellipse centered at (0, 0) with vertices along the y -axis with (x y -coordinates) (0, ±3) and whose minor axis has endpoints with (x y -coordinates) (±2, 0). We graph it below. 2 y π 3 x y π 3 x √ 21x2 + 10xy 3 + 31y 2 = 144 √ The elimination of the troublesome ‘xy ’ term from the equation 21x2 + 10xy 3 + 31y 2 = 144 in Example 11.6.1 number 2 allowed us to graph the equation by hand using what we learned in Ch...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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