• Discuss thedefinition and Equation of a
Circle.
• Learn how to find the Equation of a Circle
• Learn how to graph a circle.
Learning Objectives
Learning Objectives
3.
It is aset of all points in a plane that
are equidistant from a fixed point or
central point.
What is a Circle?
What is a Circle?
A circle isformed when a plane cuts a
cone horizontally, perpendicular to its
axis (the central line of the cone).
How a Circle Forms
How a Circle Forms
6.
Center at theorigin (0,0)
Standard Form of the Equation of a Circle
Standard Form of the Equation of a Circle
Standard Form of the Equation of a Circle
7.
Center at (h,k)
StandardForm of the Equation of a Circle
Standard Form of the Equation of a Circle
Standard Form of the Equation of a Circle
8.
Given 1.
Given 1.The endpoints of a diameter
are (-6,8) and (6,-8).
The endpoints of a diameter
are (-6,8) and (6,-8).
a. Find the standard form
b. Find the center and the radius
c. Graph the circle
9.
Given 1.
Given 1.The endpoints of a diameter
are (-6,8) and (6,-8).
The endpoints of a diameter
are (-6,8) and (6,-8).
10.
Given 1.
Given 1.The endpoints of a diameter are
(-6,8) and (6,-8).
The endpoints of a diameter are
(-6,8) and (6,-8).
11.
x² + y²= 100
Given 1.
Given 1. The endpoints of a diameter are (-6,8)
The endpoints of a diameter are (-6,8)
and (6,-8).
and (6,-8).
12.
x² + y²– 35 = -6y + 10x
Given 2.
Given 2. x² + y² – 35 = -6y + 10x
a. Find the standard form of the given equation
b. Find the center and the radius
c. Graph the circle
13.
x² + y²-35 = -6y + 10x
Given 2.
Given 2. x² + y² -35 = -6y + 10x
14.
x² + y²-35 = -6y + 10x
Given 2.
Given 2. x² + y² -35 = -6y + 10x
Center is at (h,k)
C(5,-3)
15.
x² + y²-35 = -6y + 10x
(x-5)² +( y + 3)² = 69
Given 2.
Given 2. x² + y² -35 = -6y + 10x
1. What isthe standard form of a circle?
A. ax²+by²+cx+dy+e =0
B. y=mx+b
C. (x-h)² + (y-k)² = r²
D. (x+y)² - r
18.
2. What isthe standard form of the circle
from the equation x² + 4x - 7 = -y² + 10y?
A. (x + 2)² + (y - 5)² = 36
B. (x + 2)² + (y - 5)² = 49
C. (x + 2)² + (y - 5)² = 25
D. (x - 2)² + (y + 5)² = 36
19.
3. All pointson a circle are the same distance
from the center.
True or False
20.
4. 2x² -12x + 2y² - 8y - 24 = 0
Find the center and the radius.
A circle isa special
type of conic section
formed when a plane
cuts through a cone
perpendicular to its
axis.
What is a Circle?
What is a Circle?
24.
It is definedas the set of all points in
a plane that are equidistant from a
fixed point called the center.
Standard Equation of a Circle
(x – h)² + (y – k)² = r²
What is a Circle?
What is a Circle?