Circle
Presentation by Group 5
Circle
• Discuss the definition and Equation of a
Circle.
• Learn how to find the Equation of a Circle
• Learn how to graph a circle.
Learning Objectives
Learning Objectives
It is a set of all points in a plane that
are equidistant from a fixed point or
central point.
What is a Circle?
What is a Circle?
Examples of Circles are:
Circle
TUMBLER OPENING
HULAHOOP RING
Circle
A circle is formed 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
Center at the origin (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
Center at (h,k)
Standard Form of the Equation of a Circle
Standard Form of the Equation of a Circle
Standard Form of the Equation of a Circle
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
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).
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).
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).
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
x² + y² -35 = -6y + 10x
Given 2.
Given 2. x² + y² -35 = -6y + 10x
x² + y² -35 = -6y + 10x
Given 2.
Given 2. x² + y² -35 = -6y + 10x
Center is at (h,k)
C(5,-3)
x² + y² -35 = -6y + 10x
(x-5)² +( y + 3)² = 69
Given 2.
Given 2. x² + y² -35 = -6y + 10x
Short Activity
Short Activity
1. What is the 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
2. What is the 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
3. All points on a circle are the same distance
from the center.
True or False
4. 2x² - 12x + 2y² - 8y - 24 = 0
Find the center and the radius.
5. 2x² - 12x + 2y² - 8y - 24 = 0
Graph the circle.
Summary
Summary
A circle is a 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?
It is defined as 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?

Circle_20250716_083932_0000.pdf a presentation about circle.

  • 1.
  • 2.
    • 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?
  • 4.
    Examples of Circlesare: Circle TUMBLER OPENING HULAHOOP RING Circle
  • 5.
    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
  • 16.
  • 17.
    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.
  • 21.
    5. 2x² -12x + 2y² - 8y - 24 = 0 Graph the circle.
  • 22.
  • 23.
    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?