Question

a whisper volume as a room that allows two people to stand on opposite side of the template luckily shape long and hear each other's Whispers. The locations at which they can hear one another are the foci of the ellipse. If the room has a major axis 122 ft and a minor axis of 22 ft, how far apart, in feet, are the two people?​

Answer 1

Answer: 120 ft

Explanation:

The Ellipse equation is:
`((x-h)^2)/(a^2)-((y-k)^2)/(b^2)=1` where

• (h, k) is the center
• "a" is the horizontal radius
• "b" is the vertical radius
• c is the distance from the center to the foci: |a² - b²| = c²

Given: horizontal diameter = 122 → horizontal radius = 61 = a

vertical diameter = 22 → vertical radius = 11 = b

Foci (c): 61² - 11² = c²

3721 - 121 = c²

3600 = c²

±60 = c

Let (h, k) = (0, 0)

Then the foci are located at -60 and +60.

The distance between them is 60 + 60 = 120