Question: An ellipse has a focal property such that a light ray or sound wave emanating from one focus will be reflected through the other focus.

An ellipse has a focal property such that a light ray or sound wave emanating from one focus will be reflected through the other focus. Many buildings, such as Statuary Hall in the U.S. Capitol and the Taj Mahal, are built with elliptical ceilings with the property that a sound from one focus is easily heard at the other focus. If a building has a ceiling whose cross sections are part of an ellipse that can be described by the equation 36x²+ 225y² = 8100 (measurements in meters), how far apart must two persons stand in order to whisper to each other using this focal property?

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