A series of free, online video lessons with examples and solutions to help Algebra
students learn about circle conic sections.

The following diagram shows how to derive the equation of circle (x - h)^{2} + (y - k)^{2} = r^{2} using Pythagorean Theorem and distance formula. Scroll down the page for examples and solutions.

**Circle Conic Section**

When working with circle conic sections, we can derive the equation of a circle by using coordinates and the distance formula.

The equation of a circle is (x - h)^{2} + (y - k)^{2} = r^{2} where r is equal to the radius, and the coordinates (x,y) are equal to the circle center.

The variables h and k represent horizontal or vertical shifts in the circle graph.

Examples:

1. Find the center and the radius

a) x^{2} + (y + 2)^{2} = 121

b) (x + 5)^{2} + (y - 10)^{2} = 9

2. Find the equation the circle with

a) center(-11, -8) and radius 4

b) center (2, -5) and point on circle(-7, -1)

**How to graph a circle in standard form and general form?**

Identify the equation of a circle.

Write the standard form of a circle from general form.

Graph a circle.

A circle is the set of points (x,y) which are a fixed distance r, the radius, away from a fixed point (h,k), the center.

(x - h)^{2} + (y - k)^{2} = r^{2}

Examples:

1. Graph the circle

a) (x - 3)^{2} + (y + 2)^{2} = 16

b) x^{2} + (y - 1)^{2} = 4

2. Write in standard form and then graph

2x^{2} + 2y^{2} - 12x + 8y - 24 = 0

**Conic Sections**

Introduction to Circles

Understand the equation of a circle

**Graph and write equations of circles**

Example:

Graph the equation

(x - 1)^{2} + (y + 2)^{2} = 9

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

When working with circle conic sections, we can derive the equation of a circle by using coordinates and the distance formula.

The equation of a circle is (x - h)

The variables h and k represent horizontal or vertical shifts in the circle graph.

Examples:

1. Find the center and the radius

a) x

b) (x + 5)

2. Find the equation the circle with

a) center(-11, -8) and radius 4

b) center (2, -5) and point on circle(-7, -1)

Identify the equation of a circle.

Write the standard form of a circle from general form.

Graph a circle.

A circle is the set of points (x,y) which are a fixed distance r, the radius, away from a fixed point (h,k), the center.

(x - h)

Examples:

1. Graph the circle

a) (x - 3)

b) x

2. Write in standard form and then graph

2x

Introduction to Circles

Understand the equation of a circle

Example:

Graph the equation

(x - 1)

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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