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Pre-Calc Homework Solutions 459

# Pre-Calc Homework Solutions 459 - Appendix A5.1 28 Original...

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28. Original parabola: y 2 5 4 x ; vertex is (0, 0); y 2 5 4 x 4 p 5 4 p 5 1, so focus is (1, 0) and directrix is x 5 2 1. New parabola: ( y 1 3) 2 5 4( x 1 2); vertex is ( 2 2, 2 3), focus is ( 2 1, 2 3), directrix is x 5 2 3. 29. Original ellipse: } x 6 2 } 1 } y 9 2 } 5 1; vertices are (0, 3) and (0, 2 3); c 2 5 9 2 6 c 5 ˇ 3 w foci are (0, 6 ˇ 3 w ); center is (0, 0). New ellipse: } ( x 1 6 2) 2 } 1 } ( y 1 9 1) 2 } 5 1; vertices are ( 2 2, 2) and ( 2 2, 2 4); foci are ( 2 2, 2 1 6 ˇ 3 w ); center is ( 2 2, 2 1). 30. Original hyperbola: } x 4 2 } 2 } y 5 2 } 5 1; vertices are (2, 0) and ( 2 2, 0); c 2 5 4 1 5 c 5 3 foci are (3, 0) and ( 2 3, 0); center is (0, 0); asymptotes are y 5 6 } ˇ 2 5 w } x . New hyperbola: } ( x 2 4 2) 2 } 2 } ( y 2 5 2) 2 } 5 1; vertices are (4, 2) and (0, 2); foci are (5, 2) and ( 2 1, 2); center is (2, 2); asymptotes are y 5 6 } ˇ 2 5 w } ( x 2 2) 1 2. 31. Original hyperbola: y 2 2 x 2 5 1; vertices are (0, 1) and (0, 2 1); c 2 5 1 1 1 c 5 ˇ 2 w foci are (0, 6 ˇ 2 w ); center is (0, 0); asymptotes are y 5 6 x . New hyperbola: ( y 2 1) 2 2 ( x 1 1) 2 5 1; vertices are ( 2 1, 2) and ( 2 1, 0); foci are ( 2 1, 1 6 ˇ 2 w ); center is ( 2
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