February 23, 2017
Obj: To find the lengths of segments that intersect in the
interior and exterior of a circle.
HW:
Questions???
HR: (10.7) Pg.754: 7-21odd, 24
February 23, 2017
February 23, 2017
February 23, 2017
February 23, 2017
February 23, 2017
February 23, 2017
February 23, 2017
February 23, 2017
February 23, 2017
(10.8) Equations of Circles
Objective: To write the equation of a circle and graph it on a
coordinate plane.
Why: Communication towers cover a circular area that can be
modeled by an equation.
February 23, 2017
Obj: To write the equation of a circle and graph it on a
coordinate plane.
Equation of a Circle in Standard Form:
(x - h)2 + (y - k)2 = r2
Center: (h, k); radius = r
r
(h,k)
(x,y)
February 23, 2017
Obj: To write the equation of a circle and graph it on a
coordinate plane.
State the center and radius of the following circles.
1. (x - 3)2 + (y + 4)2 = 25
2. x2 + (y - 3)2 = 9
3.
x2
+
y2 = 49
February 23, 2017
Write the equation of each circle.
Obj: To write the equation of a circle and graph it on a
coordinate plane.
1. center (3, -3) and radius = 6
2. center at (0, 1) and diameter = 3
3. diameter endpoints (-1,2) and (7,8)
February 23, 2017
Factor.
Obj: To write the equation of a circle and graph it on a
coordinate plane.
x2 + 10x + 25
x2 - 6x + 9
x2 + 8x + 16
x2 -4x + 4
February 23, 2017
Obj: To write the equation of a circle and graph it on a
coordinate plane.
Write the equation in standard form by completing the square.
Then state the center and radius.
x2 + y2 + 8x - 14y + 40 = 0
February 23, 2017
Obj: To write the equation of a circle and graph it on a
coordinate plane.
Write the equation in standard form by completing the square.
Then state the center and radius.
x2 + y2 - 4x + 6y = -9
February 23, 2017
Obj: To write the equation of a circle and graph it on a
coordinate plane.
Find the point(s) of intersection between x2 + y2 = 2 and y = -x+2.
February 23, 2017
How do you locate the center of a circle?
Obj: To write the equation of a circle and graph it on a
coordinate plane.
February 23, 2017
Obj: To write the equation of a circle and graph it on a
coordinate plane.
Strategically located substations are extremely important in the
transmission and distribution of a power company's electric supply.
Suppose three substations are modeled by the points D(-8,3),
E(-4,7), and F(-4,-1). Determine the location of a town equidistant
from all three substations, and write the equation for the circle.
E(-4,7)
D(-8,3)
F(-4,-1)
February 23, 2017
Circle J is located in the first quadrant with center (a,b) and radius s. Carl
transforms Circle J to prove that it is similar to any circle centered at the origin
with radius t. Which sequence of transformations did Carl use?
A. Translate Circle J by (x,y) (x+a, y+b) and dilate by a factor of
t
s
.
s
B. Translate Circle J by (x,y) (x+a, y+b) and dilate by a factor of
C. Translate Circle J by (x,y) (x-a, y-b) and dilate by a factor of
t
t
.
.
s
D. Translate Circle J by (x,y) (x-a, y-b) and dilate by a factor of
s
t
.
February 23, 2017
Obj: To write the equation of a circle and graph it on a
coordinate plane.
HF:
(HR) (10.8) Pg.760: 13-35odd, 40