1. What is the equation of a parabola with the given vertex and focus?
Vertex: (1,6) Focus: (1,8)
2. A radio station has a broadcast area in the shape of a circle with equation x2 + y2 = 1296
a. State the radius in miles
b. Find the intercepts of the graph
c. What is the area of the region in which the broadcast from the station can be picked up?
1. The equation of a parabola with vertex (h,k) and focus (h, k+p) is given by (x-h)^2 = 4p(y-k).
In this case, the vertex is (1,6) and the focus is (1,8), so the equation would be (x-1)^2 = 8(y-6).
2.
a. The radius of the circle is given by the square root of 1296, which is 36 miles.
b. To find the intercepts, we set y = 0 and solve for x:
x^2 + 0 = 1296
x^2 = 1296
x = ±sqrt(1296)
x = ±36
So, the x-intercepts are (-36,0) and (36,0).
c. The area of the region in which the broadcast from the station can be picked up is given by the area of the circle, which is πr^2.
So, the area = π*36^2 = π*1296 = 1296π square miles.