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Chapter 10: Q.5 (page 694)

True or False Parametric equations defining a curve are unique.

Short Answer

Expert verified

False

Step by step solution

01

Step 1. Description

Given Parametric equations defining a curve are unique.

We have to find out if it is true or false.

02

Step 2. Simplification

False,

for example:

$x (t) = \sin t, y (t) = \cos t r e p r e s e n t t h e u n i t c i r c l e x^{2} + y^{2} = 1 x (t) = \sqrt{t}, y (t) = \sqrt{1 - t}, r e p r e s e n t t h e u n i t c i r c l e x^{2} + y^{2} = 1$

so the statement in the question given is false.

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Most popular questions from this chapter

In Problems 63– 66, graph each function by hand. Be sure to label any intercepts

$f (x) = \sqrt{- 1 + x^{2}}$

In Problems 67–74, analyze each conic

$\frac{{(x - 3)}^{2}}{4} - \frac{y^{2}}{25} = 1$

If $θ$ is acute, the Half-angle Formula for the sine function isrole="math" localid="1646654694239" $\sin \frac{θ}{2} =______$ .

Find an equation for each ellipse. Graph the equation by hand.

Center at $(1, 2)$ : focus at $(1, 4)$ : contains the point $(2, 2)$

The graph of a parabola is given. Match each graph to its equation.

$A) y^{2} = 4 x C) y^{2} = - 4 x E) {(y - 1)}^{2} = 4 (x - 1) G) {(y - 1)}^{2} = - 4 (x - 1) B) x^{2} = 4 y D) x^{2} = - 4 y F) {(x + 1)}^{2} = 4 (y + 1) H) {(x + 1)}^{2} = 4 (y + 1)$

See all solutions

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