# Calculus 2 : Parametric, Polar, and Vector

## Example Questions

### Example Question #41 : Parametric

Given  and , what is  in terms  (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 #42 : Parametric

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 #43 : Parametric

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 #44 : Parametric

Convert the following equation from parametric to rectangular coordinates:

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:

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:

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:

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)?

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 #49 : Parametric

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 #50 : Parametric

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