Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #15 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

We know that  and , so we can solve both equations for :

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

Example Question #16 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above.

Correct answer:

Explanation:

We know   and  , so we can solve both equations for :

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

 

Example Question #17 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above.

Correct answer:

Explanation:

We know   and , so we can solve both equations for :

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

 

 

 

Example Question #18 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above.

Correct answer:

Explanation:

We know  and , so we can solve both equations for :

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

 

Example Question #19 : Parametric Form

Convert the following parametric function into rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To eliminate the parameter, we can solve for t in terms of y easiest:

Next, substitute all of the t's in the equation for x with what we defined above:

To finish, subtract 3, multiply by 4 and take the square root of both sides. We need plus or minus because both positive and negative squared give a positive result. 

Example Question #20 : Parametric Form

If  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and , we can find the rectangular form by solving both equations for :

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

 

Example Question #21 : Parametric Form

If  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above 

Correct answer:

Explanation:

Given  and , we can find the rectangular form by solving both equations for :

 

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

Example Question #22 : Parametric Form

If  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and , we can find the rectangular form by solving both equations for :

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

Example Question #23 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Since we have  and , let's solve each equation for :

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

Example Question #24 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Since we have   and , let's solve each equation for :

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

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