The height of the tunnel at the center is 27 ft and the vertical clearance must be 9 ft at a point 24 ft from the center. Find an equation for the ellipse.

Is this correct

Center = (0,0) | Points = (0,27), (-24,9), (24,9) | Vertex = (0,27)
(y/a)^2 + (x/b)^2
= (9/27)^2 + (24/b)^2 = 1
b^2 = 648
---
y^2/729 + x^2/648 = 1

Question

The height of the tunnel at the center is 27 ft and the vertical clearance must be 9 ft at a point 24 ft from the center. Find an equation for the ellipse.

Is this correct

Center = (0,0) | Points = (0,27), (-24,9), (24,9) | Vertex = (0,27)
(y/a)^2 + (x/b)^2
= (9/27)^2 + (24/b)^2 = 1
b^2 = 648
---
y^2/729 + x^2/648 = 1

neer2890 · Answer

ellipse with centre at (0,0) and major axis =2a and minor axis =2b
$$\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2} }=1$$
|dw:1404470560480:dw|

anonymous · Answer

This is what I have now:

24^2/b^2 + 9^2/27^2 = 1
24^2/b^2 = 8/9
24^2/*b^2 = 8/9
8/9*b^2 = 576
b^2 = 648
---
x^2/648 + y^2/729

mathmate · Answer

Your answer is mathematically correct.
The best way to solve this type of problems is to do what @neer2890 did: draw a diagram and put numbers in so you can visualize the problem and anticipate the solution graphically.  This will help you visualize your next problem, and come up with a logical solution.
|dw:1404474762726:dw|
This looks like a wide tunnel which is rather expensive to construct.
 Double-check the question to see if the tunnel is 24 ft. high at 9 ft from the centre!