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Suppose a curve is given by the parametric equations x=f(t), y=g(t), where the range of f is [2,...

Question:

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}[2,\ 5] {/eq} and the range of {eq}g {/eq} is {eq}[2,\ 5] {/eq}. What can you say about the curve? You must select all correct choices to get full credit on this problem.range of {eq}g {/eq} is {eq}[-1,\ 10] {/eq}. What can you say about the curve? Select ALL correct choices.

A. The curve must lie outside the rectangle {eq}[2,\ 5] {/eq} by {eq}[2,\ 5] {/eq}.

B. The curve is a circle with center {eq}(2,\ 2) {/eq} and radius 5.

C. The curve is the line with endpoints {eq}(2,\ 2) {/eq} and {eq}(6,\ 5) {/eq}.

D. Nothing can be said about the curve.

E. The curve is completely contained in the rectangle {eq}[2,\ 5] {/eq} by {eq}[2,\ 5] {/eq}.

F The curve must lie inside a circle with center {eq}(2,\ 2) {/eq} and radius 0.5.

Parametric Curves:

{eq}\\ {/eq}

For the parametric curve of the form {eq}x=f(t), y=g(t) {/eq}, where the range of {eq}f {/eq} is {eq}[a,b] {/eq} and range of {eq}g {/eq} is {eq}[a,b] {/eq}, the region is enclosed in the rectangle with vertices {eq}(a,a),(b,a),(a,b) \ \&(b,b). {/eq}

Answer and Explanation:

{eq}\\ {/eq}

It is clear that the curve lies inside the rectangle with vertices {eq}(2,2),(2,5),(5,2) \ \& (5,5) {/eq} i.e. curve is completely contained in the rectangle {eq}[2,\ 5] {/eq} by {eq}[2,\ 5] {/eq}.

So, option {eq}(E) {/eq} is correct.


Learn more about this topic:

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Parametric Equations in Applied Contexts

from Precalculus: High School

Chapter 24 / Lesson 6
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