To write an equation for a parabola with a vertex at the origin, we can use the standard form equation of a parabola: \(y = ax^2\).
Since the parabola opens upward, the coefficient \(a\) must be positive.
Given that the pipe is located 2 inches from the vertex of the mirror, we know that the distance from the focus to the vertex (which is also the distance from the focus to the directrix) is 2 inches.
In a parabolic geometry, the distance from the focus to the vertex is equal to \(1/(4a)\). Therefore, we have:
\(\frac{1}{4a} = 2\)
Simplifying this equation, we can solve for \(a\):
\(a = \frac{1}{8}\)
Therefore, the equation of the parabola is:
\(y = \frac{1}{8}x^2\)
a mirror with a parabolic cross section is used to collect sunlight on pipe located at the focus of the mirror the pipe is located 2 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 answer
1 answer