### All Precalculus Resources

## Example Questions

### Example Question #111 : Understand Features Of Hyperbolas And Ellipses

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

For the given hypebola in the question, the transverse axis is horizontal and its center is located at .

Next, find .

The foci are then located at and .

### Example Question #1 : Hyperbolas

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

For the given hypebola in the question, the transverse axis is horizontal and its center is located at .

Next, find .

The foci are then located at and .

### Example Question #112 : Understand Features Of Hyperbolas And Ellipses

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

First, put the given equation in the standard form of the equation of a hyperbola.

Group the terms together and the terms together.

Next, factor out from the terms and from the terms.

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

Subtract from both sides.

Divide both sides by .

Factor both terms to get the standard form for the equation of a hyperbola.

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

For the given hypebola in the question, the transverse axis is horizontal and its center is located at .

Next, find .

The foci are then located at and .

### Example Question #5 : Hyperbolas

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

First, put the given equation in the standard form of the equation of a hyperbola.

Group the terms together and the terms together.

Next, factor out from the terms and from the terms.

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

Subtract from both sides.

Divide both sides by .

Factor both terms to get the standard form for the equation of a hyperbola.

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

Next, find .

The foci are then located at and .

### Example Question #113 : Understand Features Of Hyperbolas And Ellipses

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

First, put the given equation in the standard form of the equation of a hyperbola.

Group the terms together and the terms together.

Next, factor out from the terms and from the terms.

Complete the squares. Remember to add the same amount to both sides of the equation!

Add to both sides.

Divide both sides by .

Factor both terms to get the standard form of the equation of a hyperbola.

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

For the given hypebola in the question, the transverse axis is vertical and its center is located at .

Next, find .

The foci are then located at and .

### Example Question #114 : Understand Features Of Hyperbolas And Ellipses

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

First, put the given equation in the standard form of the equation of a hyperbola.

Group the terms together and the terms together.

Next, factor out from the terms and from the terms.

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

Add to both sides.

Divide both sides by .

Factor both terms to get the standard form of the equation of a hyperbola.

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

For the given hypebola in the question, the transverse axis is vertical and its center is located at .

Next, find .

The foci are then located at and .

### Example Question #115 : Understand Features Of Hyperbolas And Ellipses

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

For the given hypebola in the question, the transverse axis is vertical and its center is located at .

Next, find .

The foci are then located at and .

### Example Question #116 : Understand Features Of Hyperbolas And Ellipses

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

Next, find .

The foci are then located at and .

### Example Question #211 : Conic Sections

Find the foci of the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

Next, find .

The foci are then located at and .

### Example Question #212 : Conic Sections

Find the foci for the hyperbola with the following equation:

**Possible Answers:**

**Correct answer:**

Recall that the standard formula of a hyperbola can come in two forms:

and

, where the centers of both hyperbolas are .

When the term with is first, that means the foci will lie on a horizontal transverse axis.

When the term with is first, that means the foci will lie on a vertical transverse axis.

To find the foci, we use the following:

For a hyperbola with a horizontal transverse access, the foci will be located at and .

For a hyperbola with a vertical transverse access, the foci will be located at and .

Next, find .

The foci are then located at and .

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