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blsea [12.9K]
3 years ago
5

A ceiling light has a cross-section in the shape of a parabola. The parabola is 24 cm wide and 9 cm deep. The lightbulb is locat

ed at the focus of the parabola. How far from the vertex is the lightbulb?

Mathematics
1 answer:
Sedbober [7]3 years ago
4 0

Answer:

  4 cm

Step-by-step explanation:

The equation of a parabola with its vertex at the origin can be written as ...

  y = 1/(4p)x^2

The problem statement tells us that one point on the parabola is (x, y) = (12, 9). We can put these values into the equation and solve for p, the distance from the focus to the vertex.

  9 = 1/(4p)(12^2)

  9×4/144 = 1/p = 1/4 . . . . . . . . multiply by the inverse of the coefficient of 1/p

Then p = 4, and the bulb is 4 cm from the vertex.

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