To find the intercepts of the graph, we need to set either x or y to zero and solve for the other variable.
1. Setting x = 0:
0 + y^2 = 5625
y^2 = 5625
y = ±75
Therefore, the y-intercepts are at (0, 75) and (0, -75).
2. Setting y = 0:
x^2 + 0 = 5625
x^2 = 5625
x = ±75
Therefore, the x-intercepts are at (75, 0) and (-75, 0).
To find the radius, we note that the equation of the circle is x^2 + y^2 = r^2, where r is the radius. In this case, r^2 = 5625, so r = √5625 = 75 miles.
The area of the region in which the broadcast from the station can be picked up is the area of the circle, which is given by the formula A = πr^2. Substituting r = 75 into the formula, we get:
A = π(75)^2
A = 5625π square miles
Therefore, the area of the region in which the broadcast from the station can be picked up is 5625π square miles.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A radio station has a broadcast area in the shape of a circle with equation x2+y2=5,625
, where the constant represents square miles.
Find the intercepts of the graph.
State the radius in miles.
What is the area of the region in which the broadcast from the station can be picked up?
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