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Calculus 2 : Parametric Form

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Example Questions

Example Question #21 : Parametric Form

If $x=\frac{1}{t}+7$ and y=14t-3 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y=\frac{14}{x-7}-3$

$y=\frac{14}{x-7}+3$

$y=\frac{x-7}{14}+3$

$y=\frac{x-7}{14}-3$

Correct answer:

$y=\frac{14}{x-7}-3$

Explanation:

Given $x=\frac{1}{t}+7$ and y=14t-3 , we can find the rectangular form by solving both equations for :

$x=\frac{1}{t}+7\rightarrow t=\frac{1}{x-7}$

$y=14t-3\rightarrow t=\frac{y+3}{14}$

Since both equations equal , we can set them equal to each other:

$\frac{y+3}{14}=\frac{1}{x-7}$

$y+3=\frac{14}{x-7}$

$y=\frac{14}{x-7}-3$

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Example Question #22 : Parametric Form

If x=t+4 and y=5t+12 , what is in terms of (rectangular form)?

Possible Answers:

y=8x-5

y=8x+5

None of the above

y=5x-8

y=5x+8

Correct answer:

y=5x-8

Explanation:

Given x=t+4 and y=5t+12 , we can find the rectangular form by solving both equations for :

$x=t+4\rightarrow t=x-4$

$y=5t+12\rightarrow t=\frac{y-12}{5}$

Since both equations equal , we can set them equal to each other:

$\frac{y-12}{5}=x-4$

y-12=5(x-4)

y=5(x-4)+12

y=5x-20+12

y=5x-8

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Example Question #23 : Parametric Form

Given x=5t+12 and y=12t+5 , what is in terms of (rectangular form)?

Possible Answers:

$y=12\left(\frac{x+12}{5}\right)+5$

$y=12\left(\frac{x+12}{5}\right)-5$

$y=12\left(\frac{x-12}{5}\right)-5$

None of the above

$y=12\left(\frac{x-12}{5}\right)+5$

Correct answer:

$y=12\left(\frac{x-12}{5}\right)+5$

Explanation:

Since we have x=5t+12 and y=12t+5 , let's solve each equation for :

$x=5t+12\rightarrow t=\frac{x-12}{5}$

$y=12t+5\rightarrow t=\frac{y-5}{12}$

Since both equations equal , we can set them equal to each other and solve for :

$\frac{y-5}{12}=\frac{x-12}{5}$

$y-5=12\left(\frac{x-12}{5}\right)$

$y=12\left(\frac{x-12}{5}\right)+5$

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Example Question #24 : Parametric Form

Given x=3t-11 and y=6t-2 , what is in terms of (rectangular form)?

Possible Answers:

y=2x-20

y=20x+2

y=2x+20

y=20x-2

None of the above

Correct answer:

y=2x+20

Explanation:

Since we have x=3t-11 and y=6t-2 , let's solve each equation for :

$x=3t-11\rightarrow t=\frac{x+11}{3}$

$y=6t-2\rightarrow t=\frac{y+2}{6}$

Since both equations equal , we can set them equal to each other and solve for :

$\frac{y+2}{6}=\frac{x+11}{3}$

$y+2=6\left(\frac{x+11}{3}\right)$

y+2=2(x+11)

y+2=2x+22

y=2x+20

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Example Question #31 : Parametric

Given x=9t-2 and y=6t+9 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y= \frac{2}{3}(x+2)+9$

$y= \frac{3}{2}(x+2)+9$

$y= \frac{3}{2}(x+2)-9$

$y= \frac{2}{3}(x+2)-9$

Correct answer:

$y= \frac{2}{3}(x+2)+9$

Explanation:

Since we have x=9t-2 and y=6t+9 , let's solve each equation for :

$x=9t-2\rightarrow t=\frac{x+2}{9}$

$y=6t+9 \rightarrow t=\frac{y-9}{6}$

Since both equations equal , we can set them equal to each other and solve for :

$\frac{y-9}{6}=\frac{x+2}{9}$

$y-9= 6\left(\frac{x+2}{9}\right)$

$y-9= \frac{2}{3}(x+2)$

$y= \frac{2}{3}(x+2)+9$

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Example Question #32 : Parametric

Given x=6t-5 and y=3t+8 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y=\frac{x+2}{5}-8$

$y=\frac{x+2}{5}+8$

$y=\frac{x+5}{2}+8$

$y=\frac{x+5}{2}-8$

Correct answer:

$y=\frac{x+5}{2}+8$

Explanation:

Given x=6t-5 and y=3t+8 , let's solve both equations for :

$x=6t-5\rightarrow t=\frac{x+5}{6}$

$y=3t+8\rightarrow t=\frac{y-8}{3}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-8}{3}=\frac{x+5}{6}$

$y-8=3\left(\frac{x+5}{6}\right)$

$y=\frac{x+5}{2}+8$

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Example Question #33 : Parametric

Given x=t+9 and y=5t+11 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

y=5x+66

y=66+5x

y=5x-34

y=5x-66

Correct answer:

y=5x-34

Explanation:

Given x=t+9 and y=5t+11 let's solve both equations for :

$x=t+9\rightarrow t=x-9$

$y=5t+11\rightarrow t=\frac{y-11}{5}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-11}{5}=x-9$

y-11=5(x-9)

y=5(x-9)+11

y=5x-45+11

y=5x-34

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Example Question #34 : Parametric

Given x=7t-15 and y=7t+15 , what is in terms of (rectangular form)?

Possible Answers:

y=-x

y=x-30

y=x+30

y=x

None of the above

Correct answer:

y=x+30

Explanation:

Given x=7t-15 and y=7t+15 , let's solve both equations for :

$x=7t-15\rightarrow t=\frac{x+15}{7}$

$y=7t+15\rightarrow t=\frac{y-15}{7}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-15}{7}=\frac{x+15}{7}$

$\frac{y-15}{7}=7\left(\frac{x+15}{7}\right)$

y-15=x+15

y=x+30

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Example Question #35 : Parametric

If x=3t+14 and y=5t+12 , what is in terms of ?

Possible Answers:

$y=\frac{5}{3}(x+14)+12$

$y=\frac{5}{3}(x+14)-12$

$y=\frac{5}{3}(x-14)+12$

None of the above

$y=\frac{5}{3}(x-14)-12$

Correct answer:

$y=\frac{5}{3}(x-14)+12$

Explanation:

Given x=3t+14 and y=5t+12 , let's solve both equations for :

$x=3t+14\rightarrow t=\frac{x-14}{3}$

$y=5t+12\rightarrow t=\frac{y-12}{5}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-12}{5}=\frac{x-14}{3}$

$y-12=\frac{5}{3}(x-14)$

$y=\frac{5}{3}(x-14)+12$

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Example Question #36 : Parametric

If x=2t-15 and y=t+8 , what is in terms of ?

Possible Answers:

None of the above

$y=\frac{x-15}{2}+8$

$y=\frac{x-15}{2}-8$

$y=\frac{x+15}{2}-8$

$y=\frac{x+15}{2}+8$

Correct answer:

$y=\frac{x+15}{2}+8$

Explanation:

Given x=2t-15 and y=t+8 , let's solve both equations for :

$x=2t-15\rightarrow t=\frac{x+15}{2}$

$y=t+8\rightarrow t=y-8$

Since both equations equal , let's set them equal to each other and solve for :

$y-8=\frac{x+15}{2}$

$y=\frac{x+15}{2}+8$

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Calculus 2 : Parametric Form

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #21 : Parametric Form

Example Question #22 : Parametric Form

Example Question #23 : Parametric Form

Example Question #24 : Parametric Form

Example Question #31 : Parametric

Example Question #32 : Parametric

Example Question #33 : Parametric

Example Question #34 : Parametric

Example Question #35 : Parametric

Example Question #36 : Parametric

All Calculus 2 Resources

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