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1. illustrate the different types of conic sections:
parabola, ellipse, circle, hyperbola, and
degenerate cases.
2. define circle
3. determine the standard form of equation of a
circle
4. recognize the equation and important
characteristics of the different types of conic
sections
5. solve situational problems involving conic
Circle Not Not
Circle
Determine the following if it is a
representation of circle.
How could you determine that
a shape is a circle?
Circles
• It is the set of all points (x,y) in a
plane (Cartesian plane) that are
equidistant from a fixed
point(center).
Center
C(h,k)
Formulas
Distance
Formula
𝑑 = 𝑥2 − 𝑥1
2 + 𝑦2 − 𝑦1
2
Standard Form
(𝑥 − ℎ)2
+(𝑦 − 𝑘)2
= 𝑟2
C(h,k)
𝑥2
+ 𝑦2
= 𝑟2
C(0,0)
Midpoint
Formula
𝑀 =
𝑥1 + 𝑥2
2
,
𝑦1 + 𝑦2
2
Write the equation of the circle in standard form given the
following:
1. Center at origin; radius is 4
2. Endpoints of diameter:
(-6,0) and (0,-2)
Identify the radius and center of the following equation of the
circle.
3. (x+1)2 + (y+6)2 = 19
4. (x-5)2 + y2 = 9
x2 + y2 = 16
(x+3)2 + (y+1)2 = 10
C(-1,-6); r = 4.36
C(5,0); r = 3
Graph the following equations of a circle:
5. x2 = 16 - y2 6. (x+5)2 + (y-3)2 = 25
Solve the problem below.
Formulas
Distance
Formula
𝑑 = 𝑥 − ℎ 2 + 𝑦 − 𝑘 2
Standard Form
(𝑥 − ℎ)2
+(𝑦 − 𝑘)2
= 𝑟2
C(h,k)
𝑥2
+ 𝑦2
= 𝑟2
C(0,0)
Midpoint
Formula
𝑀 =
𝑥1 + 𝑥2
2
,
𝑦1 + 𝑦2
2
1. Circles.pptx
1. Circles.pptx
1. Circles.pptx

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1. Circles.pptx

  • 1. 1. illustrate the different types of conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases. 2. define circle 3. determine the standard form of equation of a circle 4. recognize the equation and important characteristics of the different types of conic sections 5. solve situational problems involving conic
  • 2.
  • 3. Circle Not Not Circle Determine the following if it is a representation of circle.
  • 4. How could you determine that a shape is a circle?
  • 5. Circles • It is the set of all points (x,y) in a plane (Cartesian plane) that are equidistant from a fixed point(center). Center C(h,k)
  • 6. Formulas Distance Formula 𝑑 = 𝑥2 − 𝑥1 2 + 𝑦2 − 𝑦1 2 Standard Form (𝑥 − ℎ)2 +(𝑦 − 𝑘)2 = 𝑟2 C(h,k) 𝑥2 + 𝑦2 = 𝑟2 C(0,0) Midpoint Formula 𝑀 = 𝑥1 + 𝑥2 2 , 𝑦1 + 𝑦2 2
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13. Write the equation of the circle in standard form given the following: 1. Center at origin; radius is 4 2. Endpoints of diameter: (-6,0) and (0,-2) Identify the radius and center of the following equation of the circle. 3. (x+1)2 + (y+6)2 = 19 4. (x-5)2 + y2 = 9 x2 + y2 = 16 (x+3)2 + (y+1)2 = 10 C(-1,-6); r = 4.36 C(5,0); r = 3
  • 14. Graph the following equations of a circle: 5. x2 = 16 - y2 6. (x+5)2 + (y-3)2 = 25
  • 16. Formulas Distance Formula 𝑑 = 𝑥 − ℎ 2 + 𝑦 − 𝑘 2 Standard Form (𝑥 − ℎ)2 +(𝑦 − 𝑘)2 = 𝑟2 C(h,k) 𝑥2 + 𝑦2 = 𝑟2 C(0,0) Midpoint Formula 𝑀 = 𝑥1 + 𝑥2 2 , 𝑦1 + 𝑦2 2