Conic Sections - Circles

What is the equation of circle?

The following diagram shows how to derive the equation of circle (x - h)² + (y - k)² = r² 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 = r² 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) x² + (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)

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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 = r²
Examples:
1. Graph the circle
a) (x - 3)² + (y + 2)² = 16
b) x² + (y - 1)² = 4

2. Write in standard form and then graph
2x² + 2y² - 12x + 8y - 24 = 0

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Conic Sections

Introduction to Circles
Understand the equation of a circle

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Graph And Write Equations Of Circles

Example:
Graph the equation
(x - 1)² + (y + 2)² = 9

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