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Calculus 2 : Parametric, Polar, and Vector

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Example Questions

Example Question #2 : Parametric Form

Given x=10t-3 and y=7t+8 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{3}{10}({x+7)+8$

$y=\frac{8}{10}({x+3)+7$

$y=\frac{8}{10}({x+7)+3$

$y=\frac{7}{10}({x+3)+8$

None of the above

Correct answer:

$y=\frac{7}{10}({x+3)+8$

Explanation:

In order to find with respect to , we first isolate in both equations:

$x=10t-3\rightarrow t=\frac{x+3}{10}$

$y=7t+8\rightarrow t=\frac{y-8}{7}$

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

$\frac{y-8}{7}=\frac{x+3}{10}$

$y-8=7(\frac{x+3}{10})$

$y=\frac{7}{10}({x+3)+8$

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Example Question #2 : Parametric Form

If x=6t+5 and y=5t+6 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{6}{5}(x-5)+6$

$y=\frac{5}{6}(x-6)+5$

None of the above

$y=\frac{5}{6}(x-5)+6$

$y=\frac{6}{5}(x-6)+5$

Correct answer:

$y=\frac{5}{6}(x-5)+6$

Explanation:

Given x=6t+5 and y=5t+6 , we can find in terms of by isolating in both equations:

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

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

Since both of these transformations equal , we can set them equal to each other:

$\frac{y-6}{5}=\frac{x-5}{6}$

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

$y=\frac{5}{6}(x-5)+6$

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Example Question #3 : Parametric Form

If x=4t-3 and y=2t+7 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{3}{x+2}+7$

$y=\frac{2}{x+3}+7$

$y=\frac{x+3}{2}+7$

$y=\frac{x+7}{3}+2$

$y=\frac{x+2}{7}+3$

Correct answer:

$y=\frac{x+3}{2}+7$

Explanation:

Given x=4t-3 and y=2t+7 , we can find in terms of by isolating in both equations:

$x=4t-3\rightarrow t=\frac{x+3}{4}$

$y=2t+7\rightarrow t=\frac{y-7}{2}$

Since both of these transformations equal , we can set them equal to each other:

$\frac{y-7}{2}=\frac{x+3}{4}$

$y-7=2\left(\frac{x+3}{4}\right)$

$y-7=\frac{x+3}{2}$

$y=\frac{x+3}{2}+7$

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Example Question #4 : Parametric Form

Given x=9t-2 and y=5t+1 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{1}{9}({x+2}})+5$

$y=\frac{2}{9}({x+5}})+1$

$y=\frac{5}{9}({x+2}})+1$

$y=\frac{9}{2}({x+5}})+1$

$y=\frac{9}{5}({x+2}})+1$

Correct answer:

$y=\frac{5}{9}({x+2}})+1$

Explanation:

Knowing that x=9t-2 and y=5t+1 , we can isolate in both equations as follows:

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

$y=5t+1\rightarrow t=\frac{y-1}{5}$

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

$\frac{y-1}{5}=\frac{x+2}{9}$

${y-1}=5(\frac{x+2}{9})$

$y=\frac{5}{9}({x+2}})+1$

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Example Question #5 : Parametric Form

Given x=t-16 and y=8t+3 , what is in terms of (rectangular form)?

Possible Answers:

y=8x+128

y=8x+15

y=8x+131

y=8x+13

y=8x+113

Correct answer:

y=8x+131

Explanation:

Knowing that x=t-16 and y=8t+3 , we can isolate in both equations as follows:

$x=t-16\rightarrow t=x+16$

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

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

$\frac{y-3}{8}=x+16$

y-3=8(x+16)

y-3=8x+128

y=8x+131

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Example Question #6 : Parametric Form

Given x=14-t and y=7t+6 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

y=7x-104

y=7-104x

y=104x-7

y=104-7x

Correct answer:

y=104-7x

Explanation:

Since we know x=14-t and y=7t+6 , we can solve each equation for :

$x=14-t\rightarrow t=14-x$

$y=7t+6\rightarrow t=\frac{y-6}{7}$

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

$\frac{y-6}{7}=14-x$

y-6=7(14-x)

y-6=98-7x

y=104-7x

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Example Question #11 : Parametric Form

Given x=2t-7 and y=4t+6 , what is in terms of (rectangular form)?

Possible Answers:

y=2x+20

y=8x+2

y=2x+6

y=6x+2

y=6x+8

Correct answer:

y=2x+20

Explanation:

Since we know x=2t-7 and y=4t+6 , we can solve each equation for :

$x=2t-7\rightarrow t=\frac{x+7}{2}$

$y=4t+6\rightarrow t=\frac{y-6}{4}$

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

$\frac{y-6}{4}=\frac{x+7}{2}$

$y-6=4\left(\frac{x+7}{2}\right)$

y-6=2(x+7)

y-6=2x+14

y=2x+20

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Example Question #12 : Parametric Form

Given x=16t-15 and y=8t+1 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{x+15}{2}-1$

$y=\frac{x+15}{2}+1$

$y=\frac{x+2}{15}+1$

None of the above

$y=\frac{x+2}{15}-1$

Correct answer:

$y=\frac{x+15}{2}+1$

Explanation:

Since we know x=16t-15 and y=8t+1 , we can solve each equation for :

$x=16t-15\rightarrow t=\frac{x+15}{16}$

$y=8t+1\rightarrow t=\frac{y-1}{8}$

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

$\frac{y-1}{8}=\frac{x+15}{16}$

$y-1=8\left(\frac{x+15}{16} \right)$

$y-1=\frac{x+15}{2}$

$y=\frac{x+15}{2}+1$

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Example Question #13 : Parametric Form

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

Possible Answers:

None of the above

y=7x+2

y=2x+7

y=2x-7

y=7x-2

Correct answer:

y=2x+7

Explanation:

We know that x=3t-2 and y=6t+3 , so we can solve both equations for :

$x=3t-2\rightarrow t=\frac{x+2}{3}$

$y=6t+3\rightarrow t=\frac{y-3}{6}$

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

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

$y-3=6(\frac{x+2}{3})$

y-3=2(x+2)

y=2(x+2)+3

y=2x+4+3

y=2x+7

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Example Question #14 : Parametric Form

Given x=4t-1 and y=t+4 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{x+1}{4}+4$

$y=\frac{x+4}{4}-1$

$y=\frac{x+4}{4}+1$

$y=\frac{x+1}{4}-4$

$y=4-\frac{x+1}{4}$

Correct answer:

$y=\frac{x+1}{4}+4$

Explanation:

We know that x=4t-1 and y=t+4 , so we can solve both equations for :

$x=4t-1\rightarrow t=\frac{x+1}{4}$

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

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

$y-4=\frac{x+1}{4}$

$y=\frac{x+1}{4}+4$

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Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #2 : Parametric Form

Example Question #2 : Parametric Form

Example Question #3 : Parametric Form

Example Question #4 : Parametric Form

Example Question #5 : Parametric Form

Example Question #6 : Parametric Form

Example Question #11 : Parametric Form

Example Question #12 : Parametric Form

Example Question #13 : Parametric Form

Example Question #14 : Parametric Form

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