Question

I need help with this question please!
In some solar collectors, a mirror with a parabolic cross section is used to concentrate sunlight on a pipe, which is located at the focus of the mirror as shown in the diagram. What is an equation of the parabola that models the cross section of the mirror?
A.) what information can you get from the diagram?
B.) what information do you need to be able to write an equation that models the cross section of the mirror?

Answer 1

Thats the diagram

Answer 2

@phi

Answer 3

@jdoe0001

Answer 4

any ideas?

Answer 5

nope... Im totally stuck...

Answer 6

have you covered quadratics yet?

Answer 7

Kind of.... But math isn't really my thing.

Answer 8

the parabola is opening vertically, thus is "x" based
and it opens upwards, thus the leading term coefficient is positive

we could use something like \(\bf (x-h)^2=4p(y-k)\)
where "p" is the distance from the vertex of the parabola to the focus
if you look at the graph, that's given

Answer 9

so we could just say do so our vertex is at the origin

keep in mind that the distance from the vertex to the focus is 6

so using that much, one could write the equation of a parabola whose focus point is at 6

Answer 10

well, to be exact the focus is at (0, 6)

Answer 11

Thank you!
What would be the information that is missing?

Answer 12

well... ahemm I guess the standard equation of the parabola as shown \(\bf (x-h)^2=4p(y-k)\) and the vertex maybe

Answer 13

Okay Thank you!