(a) Sketch the curves represented by:
(i) x = t/2, y = $1 - \frac { t ^ { 2 } } { 4 }$ (ii) x = sin t, y = 1 sin $2$ t
(iii) x = e $t$ , y = 1 - e $2 t$ (b) Describe the differences between the three curves in part (a).(c) Produce Cartesian equations for the curves in parts (a)(i), (ii), and (iii) by eliminating the parameter. Compare your results.

Question

Quizplus · Accepted Answer

The Answer is $(b) (i) This curve represents the entire parabola y = 1 - x ^ { 2 } . (ii) This curve represents the part of the parabola in (i) with x \in [ - 1, 1]. (iii) This curve represents the part of the parabola in (i) with 0 ≤ x. (c) They have the same Cartesian equation, y = 1 - x 2 with different domains.$ (b) (i) This curve represents the entire parabola y = 1

- x ^ { 2 }

.
(ii) This curve represents the part of the parabola in (i) with x

\in

[ - 1, 1].
(iii) This curve represents the part of the parabola in (i) with 0 ≤ x.
(c) They have the same Cartesian equation, y = 1 - x

2

with different domains.

(A) Sketch the Curves Represented By: (I) X = T/2 1−t241 - \frac { t ^ { 2 } } { 4 }1−4t2​

(A) Sketch the Curves Represented By:
(I) X = T/2 $1 - \frac { t ^ { 2 } } { 4 }$