# Hyperbolas in Standard Form Worksheets

What Are Hyperbolas in Standard Form? We can define hyperbola in a number of ways. Mathematically, we use two ways to define a hyperbola: 1. The intersection of a cone with a plane at an angle greater than the slope of the cone. 2. The set of all points such that the ratio of the distance to a single focal point divided by the distance to the line (the directrix of the hyperbola) is greater than one. 3. The set of all points such that the difference between distances to two focal points is constant. In mathematics, standard equations are those equations that are expressed in such a way that we can easily get useful information just by looking at that equation. In the case of hyperbola, we can have two different standard equations, one for the hyperbola that opens up or down and the other one for hyperbolas that open sideways. The standard form of the equation for hyperbolas that open up or down is written as (y - k)2 / a2 – (x-h)2 / b2 =1. The standard form of the equation of hyperbola that opens sideways is expressed as (x -h)2 / a2 – (y-k)2 / b2 = 1. Note that the x comes first of for hyperbolas that open sideways, and y comes first for hyperbolas that open up and down.

• ### Basic Lesson

Guides students through the beginner skills of Hyperbolas in Standard Form. Write the equation in standard form.

• ### Intermediate Lesson

Demonstrates how to use advanced skills to tackle Hyperbolas in Standard Form problems.

• ### Independent Practice 1

A really great activity for allowing students to understand the concepts of the Hyperbolas in Standard Form.

• ### Independent Practice 2

Students use Hyperbolas in Standard Form in 20 assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with 12 problems to achieve the concepts of Hyperbolas in Standard Form.

• ### Skill Quiz

This tests the students ability to understand Hyperbolas in Standard Form.