Problem

(a) Sketch the curve by using the parametric equa…

02:53

Problem 9 Easy Difficulty

(a) Sketch the curve by using the parametric equations to plot points. Indicat with an arrow the direction in which the curve is traced as $ t $ increases.
(b) Eliminate the parameter to find a Cartesian equation of the curve.

$ x = \sqrt{t} $, $ \quad y = 1 - t $

Answer

(a) $$\begin{array}{|c|ccccr|}
\hline t & 0 & 1 & 2 & 3 & 4 \\
\hline x & 0 & 1 & 1.414 & 1.732 & 2 \\
\hline y & 1 & 0 & -1 & -2 & -3 \\
\hline
\end{array}$$
(b) $x=\sqrt{t} \Rightarrow t=x^{2} \Rightarrow y=1-t=1-x^{2}$. since $t \geq 0, x \geq 0$
So the curve is the right half of the parabola $y=1-x^{2}$

Topics

Parametric Equations

Polar Coordinates

Calculus: Early Transcendentals

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Discussion

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Video Transcript

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Wen Z.