Page 176 - Math Course 3 (Book 2)

Circles: Equations

MO. 11 - L5b The center, C, appears to be at (4, 1). This is the
location of the tower. Find r by using the Distance
Problem-Solving: Graph the Formula with the center and any of the three
points.
Equation of a Circle

r = (–1–4)² + (0 – 1)²

Let’s Begin = 26

Write an equation.

26
Real World Example (x – 4)² + (y – 1)² = ( )²
(x – 4)² + (y – 1)² = 26
ELECTRICITY
Strategically located substations are extremely
important in the transmission and distribution of Check
a power company’s electric supply. Suppose three You can verify the location of the center by finding
substations are modeled by the points D(3, 6), the equations of the two bisectors and solving a
E(–1, 0), and F(3, –4). Determine the location of a system of equations. You can verify the radius by
town equidistant from all three substations, and finding the distance between the center and
write an equation for the circle. another of the three points on the circle.

c = (4, 1) midpoint of ED = (1, 3)

3 – 1 –2
slope = =
1 – 4 3
–2
y – 1 = (x – 4)
3
–2 11
y = 3 x + 3
Explore You are given three points that lie on a
circle.

Plan Graph ΔDEF. Construct the perpendicular midpoint of DF = (3, 1)
bisectors of two sides to locate the cen- 1 – 1
ter, which is the location of the tower. Find slope = = 0
4 – 3
the length of a radius. Use the center and
radius to write an equation. y = 1

–2 11
Solve Graph ΔDEF and construct the 1 = 3 x + 3
perpendicular bisectors of two sides.
3 = –2x + 11

2x = 8

x = 4
(1, 4)

r = (3 – 4)² + (6 – 1)² = 26

Answer (4,1); (x – 4)² + (y – 1)² = 26

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