anonymous one year ago 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.

1. anonymous

@ganeshie8

2. anonymous

@Hero

3. anonymous

@IrishBoy123

4. IrishBoy123

do you recognise this? $\displaystyle{\left(\frac{x}{a}\right)^2 + \left(\frac{y}{b}\right)^2} = 1$

5. anonymous

yea thats the standard form

6. anonymous

what i don't understand is the description in gives at the end

7. IrishBoy123

so you have two points on the ellipse, right?

8. anonymous

right

9. IrishBoy123

ok shall we draw? |dw:1440548805113:dw| is that how you see it?

10. IrishBoy123

so 2 points, 2 unknowns, ie a and b

11. anonymous

so the foci are (0, +/- 8) ?

12. IrishBoy123

forget about foci just plug the 2 points into the standard equation

13. anonymous

ok

14. IrishBoy123

do (0,35) first

15. anonymous

ok gimme a sec

16. anonymous

(0/a)^2 + (35/b^2) =1

17. anonymous

i solved it

18. anonymous

(x^2 / 100) + (y^2 / 1225) = 1

19. anonymous

yea ignore what i put first

20. IrishBoy123

cool here its is https://www.desmos.com/calculator/httgrdpuki but maybe write it prettier $$\displaystyle{\left(\frac{x}{10}\right)^2 + \left(\frac{y}{35}\right)^2} = 1$$

21. anonymous

lol ok thanks