Question

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 (3, 6) and top of the bulb is at (3, 4)?

Answer 1

Answer: (x - 1)^2 = -20(y - 5)

Explanation:

To determine the correct equation that represents the parabola, we need to analyze the given options and compare them to the given information. The base of the bulb is at (1, 5) and the top of the bulb is at (1, 1). We can see that the x-coordinate remains constant at 1, while the y-coordinate changes from 5 to 1. Let's examine each option: 1. (x + 1)^2 = 20(y + 5) 2. (x + 1)^2 = 16(y + 5) 3. (x - 1)^2 = -20(y - 5) 4. (x - 1)^2 = -16(y - 5) Option 1: The equation represents a parabola with the vertex at (-1, -5) and an opening upwards. It does not match the given information since the vertex should be at (1, 5). Option 2: The equation represents a parabola with the vertex at (-1, -5) and an opening upwards. It does not match the given information since the vertex should be at (1, 5). Option 3: The equation represents a parabola with the vertex at (1, 5) and an opening downwards. This matches the given information. Option 4: The equation represents a parabola with the vertex at (1, 5) and an opening downwards. This matches the given information. Based on the analysis, the correct equation that represents the parabola in which the base of the bulb is at (1, 5) and the top of the bulb is at (1, 1) is: (x - 1)^2 = -20(y - 5)

Answer 2

(x-3)² = -8(y - 6)

it's the equation of the parabola

gathmath

onlinemath4all

base = Vertex = (3,6)

top = Focus = (3,4)

parabola formula

that opens up and symmetric about

y-axis with at vertex (h, k).

(x-h)² = 4a(y - k)

h = 3 and k = 6

a = 4 - 6 = -2

(x-h)² = 4a(y - k)

(x-3)² = (4*-2)(y - 6)

(x-3)² = -8(y - 6)

= answer

= equation of the parabola