College Algebra Chapter 2 Functions and Graphs Section 2.2 Circles Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

Concepts 1. Write an Equation of a Circle in Standard Form 2. Write the General Form of an Equation of a Circle

Concept 1 Write an Equation of a Circle in Standard Form

Write an Equation of a Circle in Standard Form (1 of 4) A circle is the set of all points in a plane that are equidistant from a fixed point called the center. The fixed distance from any point on the circle to the center is called the radius.

Write an Equation of a Circle in Standard Form (2 of 4) Standard Form of Equation of a Circle:

Write an Equation of a Circle in Standard Form (3 of 4) Example: Graph a circle with center ( –3, 2 ) and radius 4. Equation: Mark the center with an open circle.

Write an Equation of a Circle in Standard Form (4 of 4) Plot points 4 units up, down, left, and right from the center. Draw the circle through the points.

Example 1 Write an equation of the circle in standard form and graph the circle. Center: (0, –3) Radius: 2 Solution:

Example 2 Write an equation of the circle in standard form and graph the circle. Center: (4, 3) Radius: 3 Solution:

Skill Practice 1 Write an equation of the circle with center (3,-1) and radius 4. Graph the circle.

Example 3 Write an equation of the circle in standard form and graph the circle. The center is (3, –2) and the circle is tangent to the y-axis r=3 Solution:

Skill Practice 2 Write the standard form of an equation of the circle with endpoints of a diameter (-3,3) and (-1,-1)

Concept 2 Write the General Form of an Equation of a Circle

Write the General Form of an Equation of a Circle (1 of 2) General Form of Equation of a Circle:

Write the General Form of an Equation of a Circle (2 of 2) To write the equation of a circle from general form into standard form, we must complete the square twice.

Example 4 Write the equation of the circle in general form: Solution:

Example (1 of 2) Write the equation of the circle in standard form. Identify the center and radius. Solution: Group the x terms, group the y terms. Move the constant term to the right.

Example (2 of 2) Complete the squares. Identify center and radius from the equation.

Example 5 Write the equation of the circle in standard form. Identify the center and radius. Solution:

Example 6 Write the equation of the circle in standard form. Identify the center and radius. Solution:

Skill Practice 3 Write the equation of the circle in standard form. Then identify the center and radius.

Determining if an Equation Represents the Graph of a Circle

Example 7 Determine if the equation represents the equation of a circle. Solution:

Skill Practice 4

Graphing a Circle on a Calculator (1 of 7) A basic graphing calculator usually requires equations in the form y = ____________ Given: Solve for y to obtain two equation

Graphing a Circle on a Calculator (2 of 7) Enter each equation.

Graphing a Circle on a Calculator (3 of 7) Graph on the standard viewing window. The graph appears distorted because of the rectangular screen on the calculator. To eliminate the distortion, go to the ZOOM menu and select ZSQUARE.

Graphing a Circle on a Calculator (4 of 7)

Graphing a Circle on a Calculator (5 of 7) ZDECIMAL will also produce a "square" window, but it is considerably smaller.

Graphing a Circle on a Calculator (6 of 7) We can zoom out once to see the entire graph.

Graphing a Circle on a Calculator (7 of 7) We can also make our own custom window.