Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #41 : Parametric

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

Possible Answers:

Correct answer:

Explanation:

Given  and , let's solve both equations for :

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

 

Example Question #42 : Parametric

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

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and , let's solve both equations for :

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

 

Example Question #43 : Parametric

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

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and  let's solve both equations for :

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

Example Question #44 : Parametric

Convert the following equation from parametric to rectangular coordinates:

Possible Answers:

Correct answer:

Explanation:

To convert the equation from parametric form to rectangular form, we must eliminate the parameter. To do this, we can solve for t with respect to x:

The plus or minus is important to remember because a square root was taken.

Now, simply plug this into the equation for y:

Example Question #45 : Parametric

Convert the following to rectangular form from parametric form:

Possible Answers:

Correct answer:

Explanation:

To convert a parametric equation into a rectangular equation, we must eliminate the parameter. We were already given an equation where t was in terms of just a variable:

Next, substitute this into the equation for x which contains t:

Finally, rearrage and solve for y:

Example Question #46 : Parametric

Convert the following equation into rectanglar form:

 

Possible Answers:

Correct answer:

Explanation:

To convert the given parametric equation into rectangualr coordinates, we must eliminate the parameter by solving for t:

Now replace t with the new term in the equation for y:

Example Question #47 : Parametric

Convert the following equation from parametric to rectangular form:

Possible Answers:

Correct answer:

Explanation:

To convert from parametric to rectangular form, eliminate the parameter (t) from one of the equations:

Now plug this into the equation for y to get our final answer:

Example Question #48 : Parametric

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

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and , let's solve both equations for :

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

Example Question #49 : Parametric

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

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and ,  let's solve both equations for :

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

Example Question #50 : Parametric

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

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and ,  let's solve both equations for :

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

 

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