Answer: [tex]x^2=32y[/tex]
Step-by-step explanation:
Given: 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 8 inches from the vertex of the mirror.
Assume the vertex is at the origin.
If the parabola opens upwards
then the coordinates of focus= (0,8)
We know that equation of parabola with focus (0,a) and open upards is of the form (vertex=(0,0)) is
[tex]x^2=4ay[/tex]
Substitute the value of a=8 in equation, we get
[tex]x^2=4\times8y[/tex]
[tex]\Rightarrow\ x^2=32y[/tex]
Therefore, equation of the parabola that models the cross section of the mirror is [tex]x^2=32y[/tex]
