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 7 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.

A y=1/28x^2
B y=1/42x^2
C y=1/35x^2
D y=1/49x^2

Answer 1

`y= (1)/(28) x^2`

Explanation:

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 7 inches from the vertex of the mirror.

The parabola is open upwards . the vertex of the parabola is (0,0)

and pipe is located 7 inches from the vertex (0,0)

7 inches is the focus of the mirror

The distance between the vertex and the focus = 7

Since parabola is upwards and vertex is (0,0) we use formula

`4py = x^2`

Where p is the distance between the vertex and focus

p = 7 we know

`4*7*y = x^2`

`28y = x^2`

Now isolate y by dividing 28 on both sides

`y= (1)/(28) x^2`