A radio station has a broadcast area in the shape of a circle with equation
x^2+y^2=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?
To find the x-intercepts, we set y=0 and solve for x:
x^2+0^2=5625
x^2=5625
x=+/-75
So the x-intercepts are (-75,0) and (75,0).
To find the y-intercepts, we set x=0 and solve for y:
0^2+y^2=5625
y^2=5625
y=+/-75
So the y-intercepts are (0,-75) and (0,75).
The radius of the circle is the square root of the constant in the equation, which is 75. So the radius is 75 miles.
The area of the circle is pi times the radius squared, which is:
A=pi*75^2
A=17,671.46
So the broadcast from the station can be picked up in an area of approximately 17,671.46 square miles.