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WZ
Numerade Educator

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Problem 12 Easy Difficulty

(a) Eliminate the parameter to find a Cartesian equation of the curve.
(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as parameter increases.

$ x = \dfrac{1}{2}\cos\theta $, $ \quad y = 2\sin\theta $, $ \quad 0 \leqslant \theta \leqslant \pi $

Answer

(a) $4 x^{2}+\frac{y^{2}}{4}=1, \quad-\frac{1}{2} \leq x \leq \frac{1}{2}, \quad 0 \leq y \leq 2$
(b) See Graph

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Video Transcript

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