A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror. The pipe is located 9 inches from the vertex of the mirror. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.(1 point)
A y = 1/81 x^2
B y = -1/36 x^2
C y = -1/81 x^2
D y = 1/36 x^2
Since the parabola opens upward and the pipe is located at the focus, we can use the standard form equation of a parabola:
y = ax^2
To find the value of a, we need to use the information given.
The pipe is located 9 inches from the vertex of the mirror, which means it is located 9 units above the x-axis.
The distance from the vertex to the focus is given by the equation:
p = 1/4a
Since the pipe is located at the focus, p = 9.
9 = 1/4a
Solving for a:
4a = 1/9
a = 1/(9*4) = 1/36
Thus, the equation of the parabola that models the cross section of the mirror is:
y = (1/36)x^2
So the correct answer is D.