The elliptical ceiling of a building is 64ft long and 24 ft

The elliptical ceiling of a building is 64ft long and 24 ft tall. Use the rectangle coordinate system to write the standard form of the equation for the elliptical ceiling. A man discovered of he stood at the focus (c,0) where c^2 =a^2 -b^2. How far along the major axis did the man stand to hear the conversations

a the standard form of the equation is __ =1

b The man stood_feet from the center of the ellipse

Reference

(-32,0) (0,24) (32,0)

It is a dome highest point is twenty four feet high from center point it is 32 feet .

Solution

standard equation of ellipse is given by

x^2 / a^2 + y^2 / b^2 = 1

2a = 64

a = 32

2b = 24

b = 12

hence equation is

(x^2 / 32^2) + (y^2 / 12^2) = 1

b)

c^2 = a^2 - b^2

plugging the values of a and b

c^2 = 1024 - 144 = 880

c = 29.66

therefore man stood 32 - 29.66 = 2 feet approx from the centre of the ellipse