Calculus 2 : Parametric Form

Example Questions

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Example Question #1 : Parametric Form

and . What is  in terms of  (rectangular form)?

Possible Answers:

Correct answer:

Explanation:

In order to solve this, we must isolate  in both equations.

and

.

Now we can set the right side of those two equations equal to each other since they both equal .

.

By multiplying both sides by , we get , which is our equation in rectangular form.

Example Question #2 : Parametric Form

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

Possible Answers:

Correct answer:

Explanation:

Given  and  , we can find  in terms of  by isolating  in both equations:

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

Example Question #3 : Parametric Form

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

Possible Answers:

None of the above

Correct answer:

Explanation:

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

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

Example Question #4 : Parametric Form

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

Possible Answers:

None of the above

Correct answer:

Explanation:

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

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

Example Question #5 : Parametric Form

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

Possible Answers:

None of the above

Correct answer:

Explanation:

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

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

Example Question #6 : 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  in terms of  by isolating  in both equations:

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

Example Question #7 : Parametric Form

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

Possible Answers:

Correct answer:

Explanation:

Given  and  , we can find  in terms of  by isolating  in both equations:

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

Example Question #8 : Parametric Form

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

Possible Answers:

Correct answer:

Explanation:

Knowing that  and , we can isolate  in both equations as follows:

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

Example Question #9 : Parametric Form

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

Possible Answers:

Correct answer:

Explanation:

Knowing that  and ,  we can isolate  in both equations as follows:

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

Example Question #10 : Parametric Form

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

Possible Answers:

None of the above

Correct answer:

Explanation:

Since we know   and ,  we can solve each equation for :

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

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