Question 1

Given the rectangular equation $$y = 2x^2$, which of the following is a valid set of parametric equations for this curve?

Accepted Answer

$$x = t$$, $$y = 2t^2$

Question 2

For the equation of a circle $$x^2$$ + $$y^2 = 25$, which parametric equations correctly represent the circle?

Accepted Answer

$$x = 5\cos t$$, $$y = 5\sin t$$

Question 3

Which step is NOT part of the standard process for converting a rectangular equation to parametric form?

Accepted Answer

Set $$y = t$$ and solve for $$x$$

Question 4

Given the ellipse equation $$\frac{x^2$}{9} + \frac{y^2$}{4} = 1$$, which parametric equations describe this ellipse?

Accepted Answer

$$x = 3\cos t$$, $$y = 2\sin t$$

Question 5

If $$x = t^2$ and y$$ = $$4(t^2 + 1$$)$$, what is the rectangular equation relating x$ and y$?

Accepted Answer

$$y = 4(x + 1)$$

Question 6

A projectile is launched such that its horizontal position is $$x(t) = 10t$$ and its vertical position is $$y(t) = -4.9t^2$ + 20t. $$Which rectangular equation relates $$x$$ and $$y$$?

Accepted Answer

$$y = -4.9\left(\frac{x}{10}\$$right)^2$$ + 20\left(\frac{x}{10}\right)$$

Question 7

Which of the following is a correct parametric representation for the line $$y = 3x + 2$$?

Accepted Answer

$$x = t$$, $$y = 3t + 2$$

Question 8

Given $$x = 2\cos t$$, $$y = 4\sin t$$, what is the rectangular equation for the curve?

Accepted Answer

$$\frac{x^2$}{4} + \frac{y^2$}{16} = 1$$

Question 9

Which parametric equations describe the motion of a point moving counterclockwise around the circle $$x^2$$ + $$y^2$$ = $$r^2$$?

Accepted Answer

$$x = r\cos t$$, $$y = r\sin t$$

Question 10

If $$x = t - 1$$ and $$y = 4(t + 1)$$, what is the rectangular equation relating $$x$$ and $$y$$?

Accepted Answer

$$y = 4(x + 2)$$

Question 11

Which parametric equations would you use to describe the ellipse $$\frac{x^2$}{a^2$} + \frac{y^2$}{b^2$} = 1$$?

Accepted Answer

$$x = a\cos t$$, $$y = b\sin t$$

Question 12

A car travels along a path described by $$x = 3t$$, $$y = 2t^2$. What is the rectangular equation for the path?

Accepted Answer

$$y = \frac{2}{9}x^2$

Question 13

Which parametric equations represent the line segment from $$(1, 2) to$$ $$(4, 8)$$?

Accepted Answer

$$x = 1 + 3t$$, $$y = 2 + 6t$$,  $$0 \leq t \leq 1$$

Question 14

Given the parametric equations $$x = t^2$, y$$ = $$t^3$$, which of the following is the correct rectangular equation?

Accepted Answer

$$y = x$$^{3/2}$$

Question 15

Which parametric equations describe the motion of a point on the ellipse $$\frac{x^2$}{16} + \frac{y^2$}{9} = 1$$?

Accepted Answer

$$x = 4\cos t$$, $$y = 3\sin t$$

Question 16

If $$x = t$$ and $$y = 2t + 3$$, what is the rectangular equation relating $$x$$ and $$y$$?

Accepted Answer

$$y = 2x + 3$$

Question 17

Which parametric equations would you use to describe the circle $$x^2$$ + $$y^2$$ = $$r^2 if $$the point starts at $$(r, 0)$$ when $$t = 0$$?

Accepted Answer

$$x = r\cos t$$, $$y = r\sin t$$

Question 18

Given $$x = 2\sin t$$, $$y = 3\cos t$$, what is the rectangular equation for the curve?

Accepted Answer

$$\frac{x^2$}{4} + \frac{y^2$}{9} = 1$$

Parametric Equations: Writing and Applications

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