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.

Answer 1

@misty1212

Answer 2

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

Answer 3

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

Answer 4

we know \(b^2=54\) so we need \(a^2\)
plug in the numbers

Answer 5

\[\frac{8^2}{a^2}+\frac{18^2}{54}=1\] solve for \(a^2\) and that is it

Answer 6

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

Answer 7

@satellite73

Answer 8

would a=24?