G10 Math Q2- Week 8- Equation of a Circle.ppt

this is a powerpoint presentation for grade 10 learners in mathematics about equation of a circle. where the general form is given and they have to convert it to standard form in order to find the center and radius of the circle

2. (Lesson Objectives)
•Transform the equation of a circle from
general form to standard form.
•Identify the center and radius of a circle from
its equation
•Demonstrates critical and creative thinking
through solving, reasoning, and explaining.
•Cooperate effectively in group and individual
activities that connect math to real-life
context.

3. Activity 1.Name that Shape!

4. What is the common shape?
What describes its size?
What tells its position?
How do we represent a circle?

5. BB

6. General Form of a Circle
x
2
+ y
2
+ Dx + Ey + F = 0

7. Standard Form of a Circle
Center is at (h, k)

2 2
2
x h y k r   
r is the radius of the circle

8. Every binomial squared has been
multiplied out.
Every term is on the left side, set
equal to 0.
2 2
: 4 6 3 0    Example x y x y
General Form of a Circle

9. Example 1 : An architect
designs a circular fountain.
Its layout is modeled by:
x
2
+ y
2
- 6x + 4y – 12 = 0
Find the center (h,k)
location and its size(radius).

10. Steps
x
2
+ y
2
- 6x + 4y – 12 = 0
(x
2
– 6x) + ( y
2
+ 4y ) = 12
( x
2
– 6x + ___) + ( y
2
+ 4y + ___) = 12
(x - 3)
2
+ (y + 2)
2
= 25
( x
2
– 6x + 9) + ( y
2
+ 4y + 4) = 12 + 9 + 4
(x – 3)
2
+ ( y – ( -2) )
2
= 25
h = 3 k = -2 r = √25 = 5

11. Example 2: Find the
center and radius of the
circle
x
2
+ y
2
– 10x + 4y + 20 = 0

12. Steps
x
2
+ y
2
- 10x + 4y + 20 = 0
(x
2
– 10x) + ( y
2
+ 4y ) = - 20
( x
2
– 10x + __) + ( y
2
+ 4y + __) = -20
(x - 5)
2
+ (y + 2)
2
= 9
( x
2
– 10x + 25) + ( y
2
+ 4y + 4) = -20+25+4
(x – 5)
2
+ ( y – ( -2) )
2
= 9
h = 5 k = -2 r = √9 = 3

13. Activity 2 : Boys Vs
Girls Relay Challenge

14. Mechanics:
Teams: Boys vs Girls
1. Each team forms a line at
the board.
2. One member completes one
step in 10 seconds, then
passes the marker.
3. Every member must
participate

15. Teams must:
✅ Transform to standard form
✅ Identify center and radius
✅ Explain what they represent
in real life

17. Scenario : Pizza
Equation : x
2
+ y
2
- 4x + 2y - 4 = 0

18. Scenario : Water Sprinkler
Equation: x
2
+ y
2
+ 6x - 8y - 11 = 0

19. Circular Garden
x
2
+ y
2
– 2x - 12y + 11 = 0

20. Questions:
In the pizza example, what do the
center and radius represent in
real life?
If you were given an equation for
your own pizza, what will be your
priority? The center or the radius?
Why do we need to
convert the equation of a
circle from general form to
standard form?

21. Activity 3: “Slice of Understanding”
What happens to the equation of a circle
when we convert it from general form to
standard form?
How can knowing the center and radius of
a circle help us in real-life situations, like
dividing a pizza?
Why do you think it’s important to connect
mathematical equations, like the circle, to
real life examples?

22. Activity 4 : “Circle
Challenge”

23. Assignment: