What is the focus of the parabola with the equation (x - 1)2 + 32= 8y?

Question

a. (1, 4)
b. (1, 2)
c. (-1, 6)
d. (1, 6)

Answer 1

What is the focus of the parabola with the equation
(x - 1)² + 32 = 8y?

8y = (x - 1)² + 32
8y - 32 = (x - 1)²
8(y - 4) = (x - 1)²

4p = 8
p = 2

The vertex (h, k) = (1, 4).

The directed distance from the vertex to the focus is p. The focus is (h, k + p) = (1, 4 + 2) = (1, 6).

The answer is d.

Answer 2

d 1,6 because the equation after you divide by 8 is 1/8(x-1)^2+4=y so the vertex is 1,4 then to figure out the distance to the focus you put the equation to find a. lal=1/4c 1/8=1/4c so the distance is 2 and since a is positive the focus will be up two from the vertex so 1,6 is the focus.

Answer 3

4p = 8 => p = 2
vertex: (1,4)
focus: (1,4+p) = (1,6), since the parabola opens up.
Therefore, the answer is d.