2. 1.5 – Circles (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
2
2 2
3 + 2 4
x y
2 2
3 + 2 16
x 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 5
x y
2 2
4 +y 25
x
8. EX 3 Write an equation of a circle with
center (2, -9) and a radius of .
11
2
2
2
2 9 11
x y
2 2 2
+
x h y k r
2 2
2 + y+9 11
x
9. EX 4 Find the coordinates of the center and
the measure of the radius.
2 2 2
6 + 3 25
x y
10. The center is
The radius is
The equation is
5. Find the center, radius, &
equation of the circle.
(0, 0)
12
x2 + y2 = 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 0
x y x
Center: (4, 0) radius: 3
2 2
( 4) 9
x 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 9
3
9
4 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 1
16 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
18. Homework
• 1.5 - p.49 1-4, 7-43 by
4’s, 45
• Bring in textbook on
Monday
• Bring in your Notecard
for Tuesday’s Ch.1 Test