3.8 equations of circles.pptsdsdsewedcxgb

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2. Lesson Objectives
•Write the standard form of the
equation of a circle.
•Graph a circle by hand and with a
calculator using the standard form of
the equation of a circle.
•Work with the general form of an
equation of a circle.

3. Definition
A Circle is a set of
points in the xy
plane that are a
fixed distance r from
a fixed point (h,k),
where (h,k) is the
center of the circle
and r is the radius.

4. 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

5. 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

6. EX 1 Write the standard form for the equation of a
circle with center (3, -2) and a radius of 4.

2 2
2
+x h y k r  
  
22
2
3 + 2 4x y   

2 2
3 + 2 16x y  

7. EX 2 Write an equation of a circle with
center (-4, 0) and a diameter of 10.

2 2
2
+x h y k r  
 
2 2
2
4 + 0 5x y   

2
2
4+y 25x 

8. EX 3 Write an equation of a circle with
center (2, -9) and a radius of .11
  
222
2 9 11x y    

2 2
2
+x h y k r  

2 2
2+y+9 11x 

9. EX 4 Find the coordinates of the center and
the measure of the radius.

2 2
2
6 + 3 25x y  

10. The center is
The radius is
The equation is
5. Find the center, radius, &
equation of the circle.
(0, 0)
12
x
2
+ y
2
= 144

11. The center is
The radius is
The equation is
6. Find the center, radius, &
equation of the circle.
(1, -3)
7
(x – 1)
2
+ (y + 3)
2
= 49

12. 7. Graph the circle, identify
the center & radius.
(x – 3)
2
+ (y – 2)
2
= 9
Center (3, 2)
Radius of 3

13. Converting from General Form to
Standard
1.Move the x terms together and the
y terms together.
2.Move C to the other side.
3.Complete the square (as needed)
for x.
4.Complete the square(as needed)
for y.
5.Factor the left & simplify the right.

14. 2 2
( 8 ) 7  x x y
8. Write the standard equation of the circle.
State the center & radius.
2 2
8 7 0x y x   
Center: (4, 0) radius: 3
2 2
( 4) 9x y  
2 2
( 8 )16 16 7    x x y

15.   
2 2
4 6 3   x x y y
9. Write the standard equation of the circle.
State the center & radius.
2 2
4 6 3 0    x y x y
Center: (-2, 3) radius: 4

2 2
2 3 16   x y
  
2 2
4 6 9394 4      x x y y

16.   
2 2
8 2 10   x x y y
10. Write the standard equation of the circle.
State the center & radius.
2 2
2 2 16 4 20 0    x y x y

2 2
4 1 7   x y
  
2 2
8 2 1 116 16 10     x x y y
2 2
8 2 10 0    x y x y
:(4, 1) : 7 2.6 Center Radius

17. 11. Write the general form of the equation of
the circle.

2 2
4 3 36   x y
2 2
8 16 6 9 36     x x y y
2 2
8 16 6 9 36 0      x x y y
2 2
8 6 11 0    x y x y