Lesson 41
Mr. Jones
Trigonometry
Name:_________________________
Date:___________________
S.W. B. A. T: Identify the center and radius of a circle given an equation and a
graph. Write an equation of a circle in center-radius form and standard form
given the radius and the center.
DO NOW: Given the circle below. (a) Identify the center of the circle. (b) Identify the
radius of the circle.
Definitions
Circle is a set of points at a fixed distance from a fixed point.
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Radius is the distance from the center to point on the circle
Center is the fixed point within the circle.
Diameter is the length of the line segment through the center of the circle with end points on
the circle.
Equations of circle
a) Center-radius form:
(x – h)2 + (y – k)2 = r2
b) Standard form:
x2 + y2 + Dx + Ey + F = 0
Distance formula
D = √(𝒚𝟐 − 𝒚𝟏 )𝟐 + (𝒙𝟐 − 𝒙𝟏 )𝟐
Midpoint formula
𝑥1 +𝑥2 𝑦1 +𝑦2
MP = (
2
,
2
)
2
Example 1: Identify the center and radius, and write an equation of a circle for each.
a)
b)
3
Exercise 1: Identify the center and radius, and write an equation of a circle for each.
a)
b)
4
Example 2. Given the radius and center for each circle. Write an equation of the circle in
center-radius form and standard form.
a) Center = (2, 3) and radius = 4
b) Center = (-1, -6) and radius = 3
5
Exercise 2. Given the radius and center for each circle. Write an equation of the circle in
center-radius form and standard form.
a) Center = ( -4, 0) and radius = 7
b) Center = (-5. -3) and radius = √5
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EXIT
1) Explain why (x – h)2 + (y – k)2 = -4 is not the equation of a circle.
2) Convert 210° to radians.
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Lesson 41
Mr. Jones
Trigonometry
Name:_________________________
Date:___________________
Homework
Write an equation of each circle in center-radius form and standard form
1) center = (0, 0) radius = 7
2) center = (4, 3) radius = 8
3) center = (5, 3) radius = 2
8
4) center = (-2,-5) radius = √2
5) center = (-1, 6) radius = √5
6) center = (-5, 4) radius =
1
2
9
7)
8)
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