These worksheets will teach your students how to find the foci and vertices of hyperbolas.

#### What are Hyperbolas? Are you thinking that math is extremely difficult? Confused about what hyperbolas are? That's quite fine! First, calm down. Now let's take a look at what is a hyperbola is. We will follow this up by talking about specific parts of characteristics of them called foci and vertices. An easy picture for a hyperbola is two mirrored parabolas. The two halves are referred to as branches. Remember ellipses? Similar to ellipses, hyperbolas, too, have two foci and two vertices. But these foci are further from the center of the hyperbolas than the vertices. In other words, a set of all points (x, y) in a plane such that the difference of the distances between the foci and x,y is a positive constant, is known as a hyperbola. Let us take a look at what foci and vertices are. Each hyperbola has two axes of symmetry. A line segment that passes through the center of the hyperbola and has vertices as its endpoints are known as the transverse axis. The foci of hyperbola lie on the line that has the transverse axis. Perpendicular to the transverse axis lies, the conjugate axis that has the co-vertices as its endpoints. The midpoint or the intersection point of both the transverse and conjugate axes is known as the center of the hyperbola.

Hyperbolas are two smooth curves that form mirror images to one another. They look like two mountains pointed towards one another. This collection of lessons and worksheets will have you finding the foci and vertices of a hyperbola. You will also learn to write the standard equation of a hyperbola. Hyperbolas are used the prediction of the trajectory of satellite images as well as the coverage of radio signals. These worksheets explain how to find the foci and vertices of a hyperbola, and how to write a standard equation for a hyperbola. Students will calculate the foci, vertices, and co-vertices of each. Students will also convert hyperbola equations into standard form.

# Print Hyperbolas Worksheets

## Foci and Vertices of a Hyperbola Lesson

This worksheet explains how to find the foci and vertices of a hyperbola. A sample problem is solved, and two practice problems are provided.

## Practice Worksheet

Students will find the foci and vertices of a hyperbola. Ten problems are provided.

## Foci and Vertices of a Hyperbola Practice

Given a hyperbola, students will find the foci and vertices. Ten problems are provided.

## Skill Review

Students review how to find the foci and vertices of a hyperbola. A sample problem is solved.

## Foci and Vertices of a Hyperbola Practice the Skill

Students are given six hyperbolas. For each, they will find the foci and vertices of a hyperbola.

## Skill Quiz

Students will demonstrate their proficiency in finding the foci and vertices of a hyperbola. Ten problems are provided.

## Foci and Vertices of a Hyperbola Check

Students will find the foci and vertices of a hyperbola. Three problems are provided, and space is included for students to copy the correct answer when given.

## Standard Equations for Hyperbolas Lesson

This worksheet explains how to do write the standard equation for a hyperbola. A sample problem is solved, and two practice problems are provided.

## Standard Equations Worksheet

Students will write the standard equation for each hyperbola. Ten problems are provided.

## Another Practice Worksheet

Students will write the standard equation for each hyperbola. Ten problems are provided.

## Review and Practice

Students review how to write the standard equation for each hyperbola. Six practice problems are provided.

## Hyperbolas Quiz

For each hyperbola, students will write the standard equation. Ten problems are provided.

## Standard Equations for Hyperbolas Check

Students will write the standard equation for each hyperbola. Three problems are provided, and space is included for students to copy the correct answer when given.