A railroad tunnel is shaped like a semiellipse as shown below
The height of the tunnel at the center is 54 ft and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse.

Question

A railroad tunnel is shaped like a semiellipse as shown below
The height of the tunnel at the center is 54 ft and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse.

anonymous · Answer

|dw:1425849466700:dw|

anonymous · Answer

@misty1212

anonymous · Answer

i know i have the points (0,54) and (8,18)

anonymous · Answer

$$\frac{x^2}{a^2} + \frac{y^2}{b^2}=1 $$

anonymous · Answer

we know $b^2=54$ so we need $a^2$ 
plug in the numbers

anonymous · Answer

$$\frac{8^2}{a^2}+\frac{18^2}{54}=1$$ solve for $a^2$ and that is it

anonymous · Answer

i got this far, i just dont get how to solve for a.

anonymous · Answer

@satellite73

anonymous · Answer

would a=24?