Stitz-Zeager_College_Algebra_e-book

# 21 are parametric equations which trace out a circle

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Unformatted text preview: et this geometrically. 840 Applications of Trigonometry 11.6.4 Answers √ √ 1. (a) x2 + 2xy + y 2 − x 2 + y 2 − 6 = 0 becomes (x )2 = −(y − 3) after rotating counter-clockwise through θ = π . 4 y √ √ (b) 7x2 − 4xy 3 + 3y 2 − 2x − 2y 3 − 5 = 0 2 becomes (x −2) +(y )2 = 1 after rotating 9 counter-clockwise through θ = π 3 y x y x θ= y θ= π 3 π 4 x √ √ x2 + 2xy + y 2 − x 2 + y 2 − 6 = 0 √ (c) 13x2 − 34xy 3 + 47y 2 − 64 = 0 2 becomes (y )2 − (x ) = 1 after rotating 16 counter-clockwise through θ = π . 6 x √ √ 7x2 − 4xy 3 + 3y 2 − 2x − 2y 3 − 5 = 0 (d) 8x2 + 12xy + 17y 2 − 20 = 0 2 becomes (x )2 + (y4) = 1 after rotating counter-clockwise through θ = arctan(2) y y θ= y π 6 x y x θ = arctan(2) x √ 13x2 − 34xy 3 + 47y 2 − 64 = 0 x 8x2 + 12xy + 17y 2 − 20 = 0 11.6 Hooked on Conics Again 841 2 2. (a) r = 1−cos(θ) is a parabola directrix x = −2 , vertex (−1, 0) focus (0, 0), focal diameter 4 (b) r = 3 2+sin(θ) = 1 1+ 2...
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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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