# Hyperbolas- Foci and Vertices Worksheets

What Are Foci and Vertices of a Hyperbola? Do you have difficulty and get frustrated with math? Confused about what hyperbolas are? That is quite fine! First, calm down. Now let us take a look at what is a hyperbola is and what are its 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.

• ### Basic Lesson

Guides students through the beginner skills. Find the foci and vertices of the hyperbola.

• ### Intermediate Lesson

Demonstrates how to use advanced skills to tackle Hyperbolas- Foci and Vertices problems.

• ### Independent Practice 1

A really great activity for allowing students to understand the concepts of the Hyperbolas- Foci and Vertices.

• ### Independent Practice 2

Students use Hyperbolas- Foci and Vertices in 20 assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Hyperbolas- Foci and Vertices.

• ### Skill Quiz

This tests the students ability to understand Hyperbolas- Foci and Vertices.

• ### Answer Key

Answers for all lessons and independent practice.

• ### Answer Key

Answers for homework and quiz.

### What Does It Look Like?

A hyperbola is a symmetrical curve formed by the intersection of a plane with cones located on opposite sides of the same vertex. The branches of the hyperbola are present at the same distance from a line passing through a point known as the center (h,k). The points nearest to the center are known as the vertices and are located at a fixed distance from the center. Hyperbola also features a line connecting the foci, center, and vertices, which is termed as the transverse axis. A hyperbola with a vertical transverse axis and horizontal transverse axis have the equations shown below,
((x - h)2 / a2) - ((y - k)2 / b2) = 1
((y - k)2 / a2) - ((x - h)2 / b2) = 1
Considering these two equations, we have to find the values of the h, k, a, b, and c. Mathematically, the vertex is defined as the point of intersection of the line lying perpendicular to the directrix, that crosses through the focus.

#### Pie of Sorts

Question: Take a Native Alaskan and divide its circumference by its diameter what do you get?

Answer: An Eskimo Pi!