Aim #16: How do we complete the square in order to write the
equation of a circle in center-radius form?
Do Now:
1. Express as a trinomial:
2
2
a) (x - 5)
b) (x + 4)
CC Geometry H
2
2. Factor the trinomial: x + 12x + 36
3. Complete the square to solve the following equation:
2
x + 6x = 40
1. The following is the equation of a circle with radius 5 and center (1,2). Do you
2
2
see why?
x - 2x + 1 + y - 4y + 4 = 25
2. Rewrite the following equations in center-radius form:
2
2
a) x + 4x + 4 + y + 6y + 9 = 36
2
2
b) x - 10x + 25 + y + 14y + 49 = 4
3. What is the center and radius of the following circle?
2
2
x + 4x + y - 12y = 41
4. Identify the center and radius for each of the following circles:
2
2
2
a) x - 20x + y + 6y = 35
2
b) x - 3x + y - 5y =
2
2
5. Determine if the circle with equation x - 6x + y - 7 = 0 can have a radius of 4.
6. Describe the graph of each equation. Explain what the graph will look like.
2
2
a) x + y + 6x + 6y = 7
2
2
b) x + 2x + y = -1
2
2
c) x + y = -3
7. Sketch graphs of the following equations:
2
2
2
2
a) x + y + 14x - 16y + 104 = 0
b) x + y + 4x - 10y + 29 = 0
graph is a point!
2
2
8. Which translation, when applied to the center of circle x + y = 4, creates the
2
2
congruent circle x + y + 8x - 10y + 37 = 0?
center (0,0), radius 2
a. T4,5
b. T4,-5
c. T-4,-5
d. T-4,5
2
2
(x + 8x + 16) + (y - 10y + 25) = -37 + 16 + 25
2
2
(x + 4) + (y - 5) = 4
center (­4,5), radius 2
2
2
9. A circle is given by the equation x + y = 100. Which of the following points
are on the circle?
a. (0,10)
b. (-8,6)
c. (-10,-10)
d. (45,55)
e. (-10,0)
Name: ___________________
Date: _________________
Hwk. #16
CC Geometry H
1. Solve for x bycompleting the square.
2
x - 10x + 9 = 0
2. Identify the centers and radii of the following circles:
2
2
a) x + 10x + 25 + y - 8y - 8 = 0
2
2
b) (x + 25) + y = 1
2
2
c) x + 2x + y - 8y = 8
2
2
d) x - 20x + y - 10y + 25 = 0
2
2
e) x + y = 19
2
2
3. Stella says the equation x - 8x + y + 2y = 5 has a center of (4,-1) and a
radius of 5. Is she correct? Why or why not?
4. Give the center, radius, circumference and area of the circle whose equation
is: [circumference and area in terms of π]
2
2
2
a) x + y - 6x + 4y - 23 = 0
2
b) x + y + 12x - 28y = 57
Mixed Review
1) Find q and r:
qo
100o
4ro
80o
2) What are the coordinates of M ′, the image of M(-2, 4), after a
counterclockwise rotation of 90ºabout the origin?
3) Quadrilateral PQRS is a rectangle. Find x.
P
(7x ­ 4)o
S
Q
(3x + 14)o
R