a. To find the intercepts, we set x=0 and y=0 in the equation x^2 + y^2 = 5,625.
When x=0, y^2 = 5,625, so y = ±75. Therefore, the y-intercepts are at (0, 75) and (0, -75).
When y=0, x^2 = 5,625, so x = ±75. Therefore, the x-intercepts are at (75, 0) and (-75, 0).
b. The radius of the circle is the square root of the constant in the equation, so the radius is √5,625 = 75 miles.
c. The area of the region in which the broadcast from the station can be picked up is the area of the circle with radius 75 miles.
The area of a circle is given by the formula A = πr^2. Substituting r = 75 into the formula, we get A = π(75)^2 = 5625π square miles.
Therefore, the broadcast area of the radio station is 5625Ï€ square miles.