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