Pre-Calc Homework Solutions 21

# Pre-Calc Homework Solutions 21 - (b y 5 t 5 2 ˇ t w 2 5 x...

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Unformatted text preview: (b) y 5 t 5 ( 2 ˇ t w ) 2 5 x 2 The parametrized curve traces the left half of the parabola defined by y 5 x 2 (or all of the curve defined by x 5 2 ˇ y w ). 15. (a) [ 2 1, 5] by [ 2 1, 3] Initial point: (0, 0) Terminal point: None (b) y 5 ˇ t w 5 ˇ x w The parametrized curve traces all of the curve defined by y 5 ˇ x w (or the upper half of the parabola defined by x 5 y 2 ). 16. (a) [ 2 3, 9] by [ 2 4, 4] No initial or terminal point. (b) x 5 sec 2 t 2 1 5 tan 2 t 5 y 2 The parametrized curve traces all of the parabola defined by x 5 y 2 . 17. (a) [ 2 3, 3] by [ 2 2, 2] No initial or terminal point. Note that it may be necessary to use a t-interval such as [ 2 1.57, 1.57] or use dot mode in order to avoid “asymptotes” showing on the calculator screen. (b) x 2 2 y 2 5 sec 2 t 2 tan 2 t 5 1 The parametrized curve traces the left branch of the hyperbola defined by x 2 2 y 2 5 1 (or all of the curve defined by x 5 2 ˇ y 2 w 1 w 1 w )....
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