Expert: Steve Holleran - 7/25/2007

Question
I heard a difficult conics question the other day adn I was wondering if you could explain it to me.

1.The elliptical ceiling in Statuary Hall in the U.S. Capitol Building
is 96 feet long and 23 feet tall.  John Quincy Adams discovered that he
could overhear the conversations of opposing party leaders near the
left side of the chamber if he situated his desk at the focus at the
right side of the chamber.  How far from the center of the ellipse along
the major axis did Adams situate his desk?  (Round to the nearest foot.)

Thanks in advance!

Answer
Hi Jillian,

Well, we have that a= 48 (major axis), b = 23 (minor axis)
and the equation for the focal distance is

               c^2 = a^2 - b^2

where c is the distance from the center to the focus.

so           c^2 = 48^2 - 23^2 = 1775

and then c = sqrt(1775) = 43.1 , so 43 feet to the nearest foot.

Hope this is what you were looking for.

Steve Holleran