Question 1

Select the curve represented by the parametric equations.​ $$\begin{array} { l } 
x = 4 ( t + 1 ) \
y = | t - 4 |
\end{array}$$ ​

Accepted Answer

A) ​   ​ 
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   ​ 
B) ​   
C) ​   
D) ​   
E) ​

Question 2

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.​ $$\begin{array} { l } 
x = \frac { 1 } { 4 } t \\
y = t ^ { 2 }
\end{array}$$ ​

Accepted Answer

A)  $y = x ^ { 2 }$ 
B)  $y = - 4 x ^ { 2 }$ 
C)  $y = 4 x ^ { 2 }$ 
D)  $y = 16 x ^ { 2 }$ 
E)  $y = - 16 x ^ { 2 }$ 
A)  $y = x ^ { 2 }$ 
B)  $y = - 4 x ^ { 2 }$ 
C)  $y = 4 x ^ { 2 }$ 
D)  $y = 16 x ^ { 2 }$ 
E)  $y = - 16 x ^ { 2 }$

Question 3

A projectile is launched at a height of h feet above the ground at an angle of $\theta$ with the horizontal.The initial velocity is $v _ { 0 }$ feet per second,and the path of the projectile is modeled by the parametric equations $x = \left( v _ { 0 } \cos \theta \right) t \text { and } y = h + \left( v _ { 0 } \sin \theta \right) t - 16 t ^ { 2 }$ . Select the correct graph of the path of a projectile launched from ground level at the value of $\theta$ and $v _ { 0 }$ .​ $\theta = 10 ^ { \circ } , v _ { 0 } = 70$ feet per second
​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   ​ 
A) ​   
B) ​   
C) ​   
D) ​   
E) ​   ​

Question 4

Select the curve represented by the parametric equations. ​
Curtate cycloid: $$x = 4 \Theta - 2 \sin \theta , y = 4 - 2 \cos \theta$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 5

Using following result find a set of parametric equation of conic.​ $x = h + a \cos \theta , y = k + b i s n \theta$ ​ vertices: $( \pm 17,0 )$ ;foci: $( \pm 15,0 )$ ​

Accepted Answer

A)  $x = 8 \cos \theta , y = 17 \sin \theta$ 
B)  $x = 15 + 17 \cos \theta , y = 15 - 8 \sin \theta$ 
C)  $x = 8 - 15 \cos \theta , y = 17 + 15 \sin \theta$ 
D)  $x = 15 - 17 \cos \theta , y = 8 \sin \theta$ 
E)  $x = 17 \cos \theta , y = 8 \sin \theta$ 
A)  $x = 8 \cos \theta , y = 17 \sin \theta$ 
B)  $x = 15 + 17 \cos \theta , y = 15 - 8 \sin \theta$ 
C)  $x = 8 - 15 \cos \theta , y = 17 + 15 \sin \theta$ 
D)  $x = 15 - 17 \cos \theta , y = 8 \sin \theta$ 
E)  $x = 17 \cos \theta , y = 8 \sin \theta$

Question 6

Using following result find a set of parametric equation of conic. ​
Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ ​
Circle: center: $( 2,6 )$ ;radius: 8
​

Accepted Answer

A)  $$x = 6 + 8 \cos \theta , y = 6 + 2 \sin \theta$$ 
B)  $$x = 2 + 6 \cos \theta , y = 6 + 8 \sin \theta$$ 
C)  $x = 2 + 8 \cos \theta , y = 6 + 8 \sin \theta$ 
D)  $x = 8 + 2 \cos \theta , y = 6 + 2 \sin \theta$ 
E)  $x = 8 + 6 \cos \theta , y = 6 + 2 \sin \theta$ 
A)  $$x = 6 + 8 \cos \theta , y = 6 + 2 \sin \theta$$ 
B)  $$x = 2 + 6 \cos \theta , y = 6 + 8 \sin \theta$$ 
C)  $x = 2 + 8 \cos \theta , y = 6 + 8 \sin \theta$ 
D)  $x = 8 + 2 \cos \theta , y = 6 + 2 \sin \theta$ 
E)  $x = 8 + 6 \cos \theta , y = 6 + 2 \sin \theta$

Question 7

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.​ $\begin{array} { l } 
x = 3 \cos \theta \
y = 4 \sin \theta
\end{array}$ ​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $$y = \frac { x } { 4 }$$ 
D)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ 
E)  $y = \frac { x } { 3 }$ 
A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$ 
C)  $$y = \frac { x } { 4 }$$ 
D)  $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$ 
E)  $y = \frac { x } { 3 }$

Question 8

Using following result find a set of parametric equation of conic. ​
Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ ​
Circle: center: $( 8 , - 3 )$ ;radius: 5
​

Accepted Answer

A)  $x = 5 + 3 \cos \theta , y = 8 - 3 \sin \theta$ 
B)  $x = 3 + 5 \cos \theta , y = 8 - 5 \sin \theta$ 
C)  $x = 8 + 5 \cos \theta , y = 3 - 5 \sin \theta$ 
D)  $x = 8 - 5 \cos \theta , y = 3 + 5 \sin \theta$ 
E)  $x = 8 + 5 \cos \theta , y = - 3 + 5 \sin \theta$ 
A)  $x = 5 + 3 \cos \theta , y = 8 - 3 \sin \theta$ 
B)  $x = 3 + 5 \cos \theta , y = 8 - 5 \sin \theta$ 
C)  $x = 8 + 5 \cos \theta , y = 3 - 5 \sin \theta$ 
D)  $x = 8 - 5 \cos \theta , y = 3 + 5 \sin \theta$ 
E)  $x = 8 + 5 \cos \theta , y = - 3 + 5 \sin \theta$

Question 9

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.​ $\begin{array} { l } 
x = | t - 1 | \
y = t + 5
\end{array}$ ​

Accepted Answer

A)  $x = | y - 1 | \text { OR } y = x + 1 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
B)  $x = | y - 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
C)  $x = | y + 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = x + 6 , x \geq 0$ 
D)  $x = | y - 5 | \text { OR } y = x + 5 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
E)  $x = | y + 5 | \text { OR } y = x - 1 , x \geq 0 \text { and } y = - x + 5 , x \geq 0$ 
A)  $x = | y - 1 | \text { OR } y = x + 1 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
B)  $x = | y - 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
C)  $x = | y + 6 | \text { OR } y = x + 6 , x \geq 0 \text { and } y = x + 6 , x \geq 0$ 
D)  $x = | y - 5 | \text { OR } y = x + 5 , x \geq 0 \text { and } y = - x + 6 , x \geq 0$ 
E)  $x = | y + 5 | \text { OR } y = x - 1 , x \geq 0 \text { and } y = - x + 5 , x \geq 0$

Question 10

Find a set of parametric equations for the rectangular equation.​ $\begin{array} { l } 
t = 2 - x \
x = 5 y - 2
\end{array}$ ​

Accepted Answer

A)  $x = 5 + t , y = \frac { 1 } { 2 } ( 4 - t )$ 
B)  $x = 2 - t , y = \frac { 1 } { 5 } ( 4 - t )$ 
C)  $x = 2 + t , y = \frac { 1 } { 5 } ( 4 - t )$ 
D)  $x = 2 + t , y = \frac { 1 } { 5 } ( 4 + t )$ 
E)  $x = 2 + t , y = \frac { 1 } { 5 } ( t - 4 )$ 
A)  $x = 5 + t , y = \frac { 1 } { 2 } ( 4 - t )$ 
B)  $x = 2 - t , y = \frac { 1 } { 5 } ( 4 - t )$ 
C)  $x = 2 + t , y = \frac { 1 } { 5 } ( 4 - t )$ 
D)  $x = 2 + t , y = \frac { 1 } { 5 } ( 4 + t )$ 
E)  $x = 2 + t , y = \frac { 1 } { 5 } ( t - 4 )$

Exam 64: Parametric Equations

Select the curve represented by the parametric equations.​ x=4(t+1) y=|t-4| ​

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.​ x=t y= ​

Select the curve represented by the parametric equations. ​ Curtate cycloid: x=4Θ−2sin⁡θ,y=4−2cos⁡θx = 4 \Theta - 2 \sin \theta , y = 4 - 2 \cos \thetax=4Θ−2sinθ,y=4−2cosθ ​

Using following result find a set of parametric equation of conic.​ x=h+acos⁡θ,y=k+bisnθx = h + a \cos \theta , y = k + b i s n \thetax=h+acosθ,y=k+bisnθ ​ vertices: (±17,0)( \pm 17,0 )(±17,0) ;foci: (±15,0)( \pm 15,0 )(±15,0) ​

Using following result find a set of parametric equation of conic. ​ Circle: x=h+rcos⁡θ,y=k+rsin⁡θx = h + r \cos \theta , y = k + r \sin \thetax=h+rcosθ,y=k+rsinθ ​ Circle: center: (2,6)( 2,6 )(2,6) ;radius: 8 ​

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.​ x=3\theta y=4\theta ​

Using following result find a set of parametric equation of conic. ​ Circle: x=h+rcos⁡θ,y=k+rsin⁡θx = h + r \cos \theta , y = k + r \sin \thetax=h+rcosθ,y=k+rsinθ ​ Circle: center: (8,−3)( 8 , - 3 )(8,−3) ;radius: 5 ​

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve.​ x=|t-1| y=t+5 ​

Find a set of parametric equations for the rectangular equation.​ t=2-x x=5y-2 ​

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Filters

Select the curve represented by the parametric equations. x=4(t+1) y=|t-4|

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=t y=

Select the curve represented by the parametric equations. Curtate cycloid: $x = 4 \Theta - 2 \sin \theta , y = 4 - 2 \cos \theta$

Using following result find a set of parametric equation of conic. $x = h + a \cos \theta , y = k + b i s n \theta$ vertices: $( \pm 17,0 )$ ;foci: $( \pm 15,0 )$

Using following result find a set of parametric equation of conic. Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ Circle: center: $( 2,6 )$ ;radius: 8

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=3\theta y=4\theta

Using following result find a set of parametric equation of conic. Circle: $x = h + r \cos \theta , y = k + r \sin \theta$ Circle: center: $( 8 , - 3 )$ ;radius: 5

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x=|t-1| y=t+5

Find a set of parametric equations for the rectangular equation. t=2-x x=5y-2