Section 2.2 class notes_0

Section 2.2 class notes_0 - 2.2.9 Write the equation in...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
( , ) h k k h r Section 2.2 Circles A circle is the set of all points ( , ) x y in the Cartesian plane that are a fixed distance r from a fixed point ( , ) h k . The fixed distance r is called the radius of the circle and the fixed point ( , ) h k is called the center of the circle. To derive the equation of a circle, we use the distance formula that was discussed in the previous section. A circle with center ( , ) h k and radius r The standard form of an equation of a circle with center ( , ) h k and radius r is ( 29 ( 29 2 2 2 x h y k r - + - = . The standard form of an equation of a circle centered at the origin with radius r 2 2 2 x y r + = . Objective 1 : Writing the Standard Form of an Equation of a Circle Note that we can use the midpoint formula to determine the center of a circle given the endpoints of a diameter of the circle. The radius can be found using the distance formula. 2.2.7 Find the standard form of the equation of the circle with endpoints of a diameter at the points _____ and _____.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2.2.9 Write the equation in standard form for a circle with center ______ and tangent to the x-axis. Objective 2 : Sketching the Graph of a Circle Once we know the center and radius of a circle, we can easily graph the circle. For additional points, find any intercepts and plot the points. Note that the y-coordinate of the center of the circle ( 29 ( 29 2 2 1 2 9 x y-+ + = ( 2 k = -) is negative because ( 29 ( 29 2 2 2 ( 2) . y y + =- -Objective 3 : Converting the General Form of a Circle into Standard Form The general form of the equation of a circle is 2 2 Ax By Cx Dy E + + + + = where , , , ,and A B C D E are real numbers and . A B = By completing the square, the equation of a circle can be rewritten from general form to standard form. 2.2.25 Find the center, radius, and intercepts of the circle with the given equation and then sketch the graph....
View Full Document

This note was uploaded on 09/08/2011 for the course MATH 1001 taught by Professor Moshe during the Spring '09 term at LSU.

Page1 / 2

Section 2.2 class notes_0 - 2.2.9 Write the equation in...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online