Name
Date
Period
Circles
A circle is the set of all points in a plane that are equidistant from a given point in
a plane, called the center. Any segment whose endpoints are the center and a
point on the circle is a radius of the circle.
Circle formula is derived from the distance formula:
d = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
You will learn about this formula next year.
Circle Formula: (𝒙 − 𝒉)𝟐 + (𝒚 − 𝒌)𝟐 = 𝒓𝟐
Example:
(𝒙 − 𝟑)𝟐 + (𝒚 + 𝟐)𝟐 = 𝟒
Center:
Graph:
Radius:
Example: (𝒙 + 𝟏)𝟐 + (𝒚 + 𝟒)𝟐 = 𝟗
Center:
Graph:
Radius:
Example: (𝒙 − 𝟒)𝟐 + (𝒚 − 𝟐)𝟐 = 𝟐𝟓
Center:
Graph:
Radius:
Example: 𝒙𝟐 + 𝒚𝟐 = 𝟏𝟔
Center:
Radius:
Graph:
Directions: Write an equation for the circle that satisfies each
set of conditions.
1. Center (0,3); radius 7 units
2. Center (-8,7); radius ½ unit
3. Center (8,-9); tangent to y-axis
4. Center (4,2); tangent to x-axis
5. Center (-2,-5); radius √3
6. Center (5,9); radius 2√5
7. Center (0,-2); tangent to x-axis
8. Center (-6,8); tangent to y-axis
Directions: Find the center and radius of the given equation.
Then graph the circle.
9. 𝑥 2 + (𝑦 + 2)2 = 4
10. 𝑥 2 + 𝑦 2 = 144
11. (𝑥 − 3)2 + (𝑦 − 1)2 = 16
12. (𝑥 + 3)2 + (𝑦 + 7)2 = 81
13. (𝑥 − 3)2 + (𝑦 + 7)2 = 50
14. (𝑥 + 8)2 + (𝑦 − 4)2 = 32
Name
Date
Period
Solving a System Graphically & Algebraically
a) Linear Equation and Quadratic Equation
b) Linear Equation and Circle Equation
How to Solve Graphically
How to Solve Algebraically
1. 𝑦 = 𝑥 2 + 𝑥 − 2; 𝑥 + 𝑦 = 1
2. 𝑦 = 𝑥 2 + 2𝑥 − 1;
𝑦 = 3𝑥 + 5
3. 𝑦 = 𝑥 − 1; 𝑥 2 + 𝑦 2 = 25
4. (𝑥 − 2)2 + (𝑦 + 1)2 = 4; 𝑦 = −𝑥 + 3
5. 𝑥 2 + 𝑦 2 = 100; 𝑦 = 𝑥 + 2
6. 𝑥 2 − 2𝑦 = 11; 𝑦 = 𝑥 − 4
7. (𝑥 + 1)2 + ( 𝑦 − 1)2 = 16; 𝑥 = 3
8. (𝑥 − 2)2 + (𝑦 − 3)2 = 4;
𝑦 =𝑥−1
9. 𝑦 = 𝑥 2 − 2𝑥 + 2; 𝑦 − 2𝑥 = −2
10. 𝑦 = 𝑥 2 + 1;
𝑦−𝑥 =1
11. 𝑦 = 𝑥 2 − 6𝑥 + 5; 𝑦 + 7 = 2𝑥
12. 𝑦 = −𝑥 2 + 8𝑥 + 7;
𝑦 = −𝑥 − 3
13. (𝑥 − 4)2 + (𝑦 + 2)2 = 25;
14.
(𝑥 + 5)2 + (𝑦 + 4)2 = 10;
15.
𝑦 = 𝑥 2 + 1; 𝑦 = 2𝑥 + 4
𝑦 = −𝑥 + 7
𝑥 = −4