Answer:
a) [tex]\frac{x^{2}}{2352.25} + \frac{y^{2}}{529} = 1[/tex], b) [tex]c = 42.7 ft[/tex], c) [tex]A \approx 3504.447 ft^{2}[/tex]
Step-by-step explanation:
a) An Ellipse centered at origin is modelled by using this formula:
[tex]\frac{x^{2}}{a^2} +\frac{y^2}{b^2}=1[/tex]
Where [tex]a, b[/tex] represents the lengths of horizontal and vertical axis, respectively. Let consider that horizontal axis is parallel and coincident with width of Statuary Hall. So, the measures of each axis are, respectively:
[tex]a = 48.5 ft, b = 23 ft[/tex]
By substituting known variables, the equation that models the hall is:
[tex]\frac{x^{2}}{2352.25} + \frac{y^{2}}{529} = 1[/tex]
b) The distance between origin and any of the foci is:
[tex]c = \sqrt{a^{2} - b^{2}} \\c = 42.7 ft[/tex]
c) The area of ellipse can determined by applying this formula:
[tex]A = \pi \cdot a \cdot b[/tex]
[tex]A \approx 3504.447 ft^{2}[/tex]
