### All Precalculus Resources

## Example Questions

### Example Question #41 : Hyperbolas And Ellipses

The equation of an ellipse, , is . Which of the following are the correct end points of the MAJOR axis of this ellipse?

**Possible Answers:**

and

and

and

and

and

**Correct answer:**

and

First, we must determine if the major axis is a vertical axis or a horizontal axis. We look at our denominators, and , and see that the larger one is under the -term. Therefore, we know that the greater axis will be a vertical one.

To find out how far the end point are from the center, we simply take . So we know the end points will be units above and below our center. To find the center, we must remember that for ,

the center will be .

So for our equation, the center will be . units above and below the center give us and .

### Example Question #41 : Hyperbolas And Ellipses

Find the endpoints of the major axis for the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

When , the major axis is horizontal. In this case, and are the endpoints of the major axis.

When , and are the endpoints of the major axis.

For the ellipse in question, is the center. In addition, and . Since , the major axis is horizontal and the endpoints are and

### Example Question #43 : Hyperbolas And Ellipses

Find the endpoints of the major axis for the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

When , the major axis is horizontal. In this case, and are the endpoints of the major axis.

When , and are the endpoints of the major axis.

For the ellipse in question, is the center. In addition, and . Since , the major axis is vertical and the endpoints are and .

### Example Question #41 : Understand Features Of Hyperbolas And Ellipses

Find the endpoints of the major axis of the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

When , the major axis is horizontal. In this case, and are the endpoints of the major axis.

When , and are the endpoints of the major axis.

For the ellipse in question, is the center. In addition, and . Since , the major axis is vertical and the endpoints are and .

### Example Question #45 : Hyperbolas And Ellipses

Find the endpoints of the major axis of the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

When , the major axis is horizontal. In this case, and are the endpoints of the major axis.

When , and are the endpoints of the major axis.

For the ellipse in question, is the center. In addition, and . Since , the major axis is horizontal and the endpoints are and

### Example Question #46 : Hyperbolas And Ellipses

Find the endpoints of the major axis of the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

Start by putting the equation in the standard form as shown above.

Group the terms and terms together.

Factor out from the terms and from the terms.

Now, complete the squares. Remember to add the same amount to both sides of the equation!

Add to both sides.

Divide by on both sides.

Now factor both terms to get the standard form of the equation of an ellipse.

Recall that when , the major axis is horizontal. In this case, and are the endpoints of the major axis.

When , and are the endpoints of the major axis.

For the ellipse in question, is the center. In addition, and . Since , the major axis is horizontal and the endpoints are and .

### Example Question #47 : Hyperbolas And Ellipses

Find the endpoints of the major axis of the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

Start by putting the equation in the standard form as shown above.

Group the terms and terms together.

Factor out from the terms and from the terms.

Now, complete the squares. Remember to add the same amount to both sides of the equation!

Subtract from both sides.

Divide by on both sides.

Now factor both terms to get the standard form of the equation of an ellipse.

Recall that when , the major axis is horizontal. In this case, and are the endpoints of the major axis.

When , and are the endpoints of the major axis.

For the ellipse in question, is the center. In addition, and . Since , the major axis is horizontal and the endpoints are and .

### Example Question #48 : Hyperbolas And Ellipses

Find the endpoints of the minor axis of the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

When , the minor axis is horizontal. In this case, and are the endpoints of the minor axis.

When , and are the endpoints of the vertical minor axis.

For the ellipse in question, is the center. In addition, and . Since , the minor axis is horizontal and the endpoints are and

### Example Question #49 : Hyperbolas And Ellipses

Find the endpoints of the minor axis of the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

When , the minor axis is horizontal. In this case, and are the endpoints of the minor axis.

When , and are the endpoints of the vertical minor axis.

For the ellipse in question, is the center. In addition, and . Since , the minor axis is horizontal and the endpoints are and

### Example Question #50 : Hyperbolas And Ellipses

Find the endpoints of the minor axis of the ellipse with the following equation:

**Possible Answers:**

**Correct answer:**

Recall the standard form of the equation of an ellipse:

, where is the center of the ellipse.

When , the minor axis is horizontal. In this case, and are the endpoints of the minor axis.

When , and are the endpoints of the vertical minor axis.

For the ellipse in question, is the center. In addition, and . Since , the minor axis is horizontal and the endpoints are and .