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8.4 Plane Curves and Parametric Equations

Focus on evaluate a parametric point and direction of travel.

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01Eliminating the parameterWorked steps · five questions 02Finding parametric equations for a curveWorked steps · five questions 03Circular motion and projectile modelsWorked steps · five questions

Lesson brief and rules

8.4 Plane Curves and Parametric Equations

Eliminate the parameter when possible; $x(t),y(t)$ describe a point at time $t$ .

Worked example

1

01 / If

x(t)=t+3, y(t)=2t-5

, find

(x(4),y(4))

02 / Substitute

t=4

into both coordinate rules.

03 / Answer:

(7, 3)

Worked example 2 · Direction of travel

For $x=t$ and $y=4$ , as $t$ increases, which way does the point move?

$x$ increases and $y$ stays constant. Answer: Right

Read the graphs

Finding parametric equations for a curve

Graph of

y = x^{2}

as parametric equations?

Solid:

y

Let $x = t$ .

Answer: $x = t, y = t^{2}$

15 questions covering every idea, with a worked answer for each.Start practice ↗

Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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8.4 Plane Curves and Parametric Equations

Ideas in this lesson

8.4 Plane Curves and Parametric Equations

Read the graphs

Finding parametric equations for a curve