Question

a car headlight mirror is parabolic in shape with a width of 6 inches and a depth of 10 inches. how far from the vertex should the bulb be positioned if it is to be placed at the focus?

Answer 1

9/40inches.

Explanation:

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Answer 2

• 9/40 inches from the vertex

Explanation:

Parabola formula:

• (y - k)² = 4p(x - h),
• (h, k) is the vertex and focus if (h, k+ p)

We'll assume the vertex is located at the origin:

• (h, k) = (0, 0)

And we have width of 6 in, so y = ±6/2 = ±3, a depth is x = 10 in

Substitute all the numbers:

• (±3)² = 4p*10
• p = 9/40

The focus is:

• (0, 9/40)

The bulb to be placed at 9/40 in from the vertex