Question

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. Write an equation of the parabola that models the cross section of the mirror. Assume that the parabola opens upward.

Answer 1

Answer: $x^2=32y$

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

$x^2=4ay$

Substitute the value of a=8 in equation, we get

$x^2=4\times8y$

$\Rightarrow\ x^2=32y$

Therefore, equation of the parabola that models the cross section of the mirror is $x^2=32y$