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Suppose a curve is given by the parametric equations x = f ( t ) , y = g ( t ) , where the...

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Suppose a curve is given by the parametric equations {eq}x = f(t), \ y = g(t), {/eq} where the range of {eq}f {/eq} is {eq}[-1,10] {/eq} and the range of {eq}g {/eq} is {eq}[-5,3] {/eq}. What can you say about the curve? You may select more than one answer.

A. The curve is a circle with center {eq}(-1, -5) {/eq} and radius {eq}3 {/eq}.

B. The curve is completely contained in the rectangle {eq}[-1,10] {/eq} by {eq}[-5,3] {/eq}.

C. The curve is the line with endpoints {eq}(-1,-5) {/eq} and {eq}(10, 3) {/eq}.

D. Nothing can be said about the curve.

E. The curve must be outside the rectangle {eq}[-1, 10] {/eq} by {eq}[-5,3] {/eq}.

F. The curve must be inside a circle with center {eq}(-1, -5) {/eq} and radius {eq}0.5 {/eq}.

Parametric Equations:

{eq}\\ {/eq}

A function in the Cartesian Plane can be written in the Parametric form using the substitutions : {eq}x=f(t), \ y=g(t) {/eq}, where time {eq}t {/eq} is the parameter of {eq}f\&g {/eq}.

{eq}f(t) \& g(t) {/eq} usually highlights the position of particle w.r.t. time.

Answer and Explanation:

{eq}\\ {/eq}

All possible paths joining {eq}(-1,-5) \ \& (10,3) {/eq} within the rectangle formed by {eq}(-1,-5),(-1,3),(10,-5) \ \& \ (10,3) {/eq} can be the possible path traced by the curve given by the given parametric equations.

So, option {eq}(C) \ \& \ (D) {/eq} are correct.


Learn more about this topic:

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Evaluating Parametric Equations: Process & Examples

from Precalculus: High School

Chapter 24 / Lesson 3
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