The local radio tower is located 20 miles east and 12 miles north of Pamela's cabin. The radio tower has a 25 mile broadcast radius. What is

the equation in general form that describes the locations within receiving distance of the tower?

A

= + 408 - 243 + +81 = 0

- 40 - 24+39 - 51 = 0

+40 + 24 + y2 - 25 = 0

D

- - 402 - 24 + 5 + 25 = 0

x^2 + y^2 - 40x - 24y - 81 = 0

Step-by-step explanation:

We can write the equation of a circle in the form

(x-h) ^2 + (y-k) ^2 = r^2

Where (h, k) is the center and r is the radius

Assuming that Pamela's cabin is the center

(x-20) ^2 + (y - 12) ^2 = 25^2

We want to get to general form

x^2 + y^2 + Dx + Ey + F = 0,

Distributing

x^2 - 40x + 400 + y^2 - 24y + 144 = 625

x^2 + y^2 - 40x - 24y + 544 - 625 = 0

x^2 + y^2 - 40x - 24y - 81 = 0