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The inside of a flashlight surrounding the bulb is shaped like a parabola in which the base of the bulb represents the vertex and the top of the bulb represents the focus. Which of the following standard equations represents the parabola in which the base of the bulb is at (4, 6) and top of the bulb is at (4, 3)?

(x – 4)2 = –12(y – 6)
(x – 4)2 = –24(y – 6)
(x + 4)2 = 12(y + 6)
(x + 4)2 = 24(y + 6)



Answer :

Lanuel

The standard equation which represents the parabola in which the base of the bulb is at (4, 6) and top of the bulb is at (4, 3) is: A. (x - 4)² = -12(y - 6).

How to determine the equation of a parabola?

Mathematically, the standard equation with the vertex for any parabola that opens up and symmetric about the y-axis is given by:

(x - h)² = 4a(y - k)

where:

  • h and k represents the vertex.
  • a is a point.

In Geometry, the focus on the coordinate plane of a parabola is generally "n" units away from the vertex, and it's directly on the right side if it opens to the right or on the left side if it opens to the left.

Given the following data:

h = 4 and k = 6

a = 3 - 6 = -3

Substituting the given parameters into the formula, we have;

(x - h)² = 4a(y - k)

(x - 4)² = 4(-3)(y - 6)

(x - 4)² = -12(y - 6)

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