An arch is in the form of a semi-ellipse whose span is 24 feet wide. The height of the arch is 10 feet. Find the equation of the ellipse.

Question

A. x²/24 + y²/10 = 1
B. x²/144 + y²/100 = 1
C. x²/100 + y²/576 = 1
D. x²/576 - y²/100 = 1

Answer 1

 

The height of the semi-ellipse is 10.  Thus the distance from the center to the vertex (highest point) is 10

Since the arch is 24 feet wide, the distance from that vertex (widest point) to the center is 1/2 of 24, which is 12.

 

Since the distance from center is larger on the x-axis (12) than the y-axis (10), this ellipse has major axis of y.

 

The distance from the center to the major axis vertex, is the value of "a".  a = 12

The distance from the center to the minor axis vertex, is the value of "b".  b = 10

 

This ellipse is centered at the origin (0,0)

 

The base equation for ellipse with x axis major is:

 

     x²       y²

   ----  =  ----- = 1

    a²        b²

 

    x²/12² + y²/10² = 1

 

    x²/144 + y²/100 = 1

 

The answer is B.