Calculus 2 : Parametric, Polar, and Vector

Example Questions

Example Question #65 : Parametric Form

Convert the following parametric equation to rectangular form:

Explanation:

To convert from parametric to rectangular coordinates, we must eliminate the parameter by finding t in terms of x or y:

We will start by taking the exponential of both sides of the equation . Recall that .

Therefore we get,

.

Now, replace t with the above term in the equation for x:

Example Question #66 : Parametric Form

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

Explanation:

Given  and , wet's solve both equations for :

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

Example Question #67 : Parametric Form

Given  and , what is  in terms of

None of the above

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 #68 : Parametric Form

Given  and , what is  in terms of

None of the above

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 #69 : Parametric Form

Given  and , what is  in terms of

None of the above

Explanation:

Given   and , wlet's solve both equations for :

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

Example Question #70 : Parametric Form

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

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 #71 : Parametric Form

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

None of the above

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 #72 : Parametric Form

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

None of the above

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 #73 : Parametric Form

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

None of the above

Explanation:

Given  and , let's solve both equations for :

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