Whispering Gallery A room with an elliptical ceiling (called an ellipsoid, since it is 3-dimensional) forms a “whispering gallery.” Thanks to the reflective property of the ellipse, a whispered message at one focus can be heard clearly by someone standing across the room at the other focus. If the elliptical ceiling has a major axis of 120 feet and a minor axis of 72 feet, how far apart are the foci?
How can you find the distance between foci, given the major and minor axes?
Find the values of a and b. Then, use
The major axis has length
The minor axis has length
Thus
The foci are
What is the standard form equation of the ellipse shown?
The foci are on the x-axis, so the major axis is horizontal.
How can you write the equation of an ellipse given a focus and a vertex?
Find the values of a and c. Use
Since