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