1.9 Notes: Circles Lesson Objective: Recognize characteris- tics of and graph circles. CCSS: F.BF.3 Build new functions from existing functions. This is Jeopardy!!!: These are the coor- dinates to the center of a circle whose endpoints of a diameter are (-7, 2) and (-3, -2).

Lesson 1:Midpoint and Distance Formula Midpoint Formula: Distance Formula:

Lesson 2:Circles in Standard Form (x – h) 2 + (y – k) 2 = r² Center: Radius: Domain: Range:

Lesson 2:Circles in Standard Form A. Find the equation of the circle with points on the diameter of a circle at (-7, 2) and (-3, -2).

Lesson 2:Circles in Standard Form B.Give the center, radius, domain and range of (x + 5) 2 + (y – 4) 2 = 9.

Lesson 2:Circles in Standard Form C. Give the domain and range for the semi-circle on the right half of the circle (x + 5) 2 + (y – 4) 2 = 9.

Lesson 2:Circles in Standard Form D. Give the domain and range for the semi-circle on the bottom half of the circle (x + 5) 2 + (y – 4) 2 = 9.

Lesson 3: The General Form of the Equa- tion of a Circle x 2 + y 2 + Dx + Ey + F = 0 To find the center and radius: convert to standard form by completing the square

Lesson 3: The General Form of the Equation of a Circle Write in standard form, graph and find domain and range. x 2 + y 2 – 8x + 10y + 32 = 0

1.9: Do I Get It? Yes or No 1.Find the center, radius, domain and range of the circle whose equation is (x – 2) 2 + (y + 4) 2 = 9. 2.Write the standard form of the equa- tion of the circle with center (-2, 3) and point on the circle (1, 2). 3.Write in standard form, graph and find domain and range of the circle x 2 + y 2 + 4x – 6y – 23 = 0.

1.9: Do I Get It? Yes or No Answers: 1.C = (2, -4), r = 3, Domain = [-1, 5], Range = [-7, -1] 2.(x + 2) 2 + (y – 3) 2 = 10 3.(x – (-2)) 2 + (y – 3) 2 = 36, C = (-2, 3), r = 6