A railroad tunnel is shaped like a semiellipse as shown below. https://i.gyazo.com/48a130dba78fec600ab1b84c1d706dad.png The height of the tunnel at the center is 35 ft and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse.

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A railroad tunnel is shaped like a semiellipse as shown below. https://i.gyazo.com/48a130dba78fec600ab1b84c1d706dad.png The height of the tunnel at the center is 35 ft and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse.

Mathematics
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Other answers:

do you recognise this? \[\displaystyle{\left(\frac{x}{a}\right)^2 + \left(\frac{y}{b}\right)^2} = 1\]
yea thats the standard form
what i don't understand is the description in gives at the end
so you have two points on the ellipse, right?
right
ok shall we draw? |dw:1440548805113:dw| is that how you see it?
so 2 points, 2 unknowns, ie a and b
so the foci are (0, +/- 8) ?
forget about foci just plug the 2 points into the standard equation
ok
do (0,35) first
ok gimme a sec
(0/a)^2 + (35/b^2) =1
i solved it
(x^2 / 100) + (y^2 / 1225) = 1
yea ignore what i put first
cool here its is https://www.desmos.com/calculator/httgrdpuki but maybe write it prettier \( \displaystyle{\left(\frac{x}{10}\right)^2 + \left(\frac{y}{35}\right)^2} = 1\)
lol ok thanks

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