A railroad tunnel is shaped like a semiellipse as shown below.

http://prntscr.com/6svnmp

The height of the tunnel at the center is 58 ft and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse.

Question

A railroad tunnel is shaped like a semiellipse as shown below. 

http://prntscr.com/6svnmp

The height of the tunnel at the center is 58 ft and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse.

rational · Answer

yeah he is smart

nnesha · Answer

ikr! rational

sleepyjess · Answer

he's not on ;-;
I thought of him

sleepyjess · Answer

rational is smart too though :)

nnesha · Answer

yeah.

rational · Answer

let the equation of ellipse be $$\dfrac{x^2}{t} + \dfrac{y^2}{58^2}=1$$

plugin the given point $(21, 29)$ in above equation and find the value of $t$

sleepyjess · Answer

$\dfrac{441}t +\dfrac{841}{3364}=1$
t = 588

sleepyjess · Answer

Would I need to find the square root of t?

rational · Answer

That looks good. sqrt is not needed, the equation of ellipse is
$$\dfrac{x^2}{588} + \dfrac{y^2}{58^2}=1$$

sleepyjess · Answer

Oh! Thanks :) Should I square 58 for the final answer?

rational · Answer

yes above is the final equation of ellipse