### All Calculus 2 Resources

## Example Questions

### Example Question #65 : Parametric Form

Convert the following parametric equation to rectangular form:

**Possible Answers:**

**Correct answer:**

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)?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

None of the above

**Correct answer:**

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 ?

**Possible Answers:**

None of the above

**Correct answer:**

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 ?

**Possible Answers:**

None of the above

**Correct answer:**

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)?

**Possible Answers:**

**Correct answer:**

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)?

**Possible Answers:**

None of the above

**Correct answer:**

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)?

**Possible Answers:**

None of the above

**Correct answer:**

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)?

**Possible Answers:**

None of the above

**Correct answer:**

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 #74 : Parametric Form

### Find *dy/dx* at the point corresponding to the given value of the parameter without eliminating the parameter:

**Possible Answers:**

**Correct answer:**

The formula for *dy/dx *for parametric equations is given as:

From the problem statement:

If we plug in *t=3*, into the above equations:

This is one of the answer choices.

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