O Do Homework evren Rankin C Secure S17 Principles of Mathem

O Do Homework evren Rankin C Secure S17 Principles of Mathematics Homework: Section 8.1 Homework Bof B complete) Score:0 of 1 pt (X 8.1.55 to the epicenter of an earthquake are contained The locations of eroe reeeiving stations and the ditanoes of the epicenter. mype an ordered pair) r your answer in the answer box and then click Check Answer. showing HW Soone: 87.5%, 7 of 8 pts eQuestion Help (y .4 Determine the locaion of

Solution

Given

(x + 4)² + (y - 2)² = 4                (1)

(x + 2)² + (y + 1)² = 9                (2)

(x + 2)² + (y - 4)² = 4                  (3)

Since the epicenter is same for all three stations therefore the intersection of these circles will be the epicenter.  

                                  // as the distance for each station from the epicenter is given by these circle equations.

from (2) and (3)

(2) - (3) we get

(x + 2)² + (y + 1)² = 9

(x + 2)² + (y - 4)² = 4

-              -             -

(y + 1)² - (y - 4)² = 9 - 4

y² + 1 + 2y - (y² + 16 - 8y) = 5

y² + 1 + 2y - y² - 16 + 8y = 5

1 + 2y - 16 + 8y = 5

10y - 15 = 5

10y = 5 + 15

y = 20/10

y = 2

put y = 2, now from eq (3)

(x + 2)² + (2 - 4)² = 4

(x + 2)² + 4 = 4

(x + 2)² = 0

x + 2 = 0

x = -2

so the location is (-2, 2)

verifying it from eq (1)

put (-2,2) in eq (1)

(x + 4)² + (y - 2)² = 4

(-2 + 4)² + (2 - 2)² = 4

2² + 0 = 4

4 = 4

since both sides are equal hence (-2, 2) is the location of the epicenter.of the earthquake.