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anonymous
 one year ago
A railroad tunnel is shaped like a semiellipse as shown below.
A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis.
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.
I will post a pic in a second.
anonymous
 one year ago
A railroad tunnel is shaped like a semiellipse as shown below. A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis. 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. I will post a pic in a second.

This Question is Closed

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1hey gave 2 points, and it is centered at the origin. x^2 / a^2 + y^2 / b^2 = 1 use the two points to find a and b....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0plug in values for x and y?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1yeah.. as a check , one of the points is already on the y axis

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(0,54) is good right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00^2/a^2 so that cancels out and I have: 54^2/b^2 = 1

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1yeah it crosses the y axis at 54, so that checks out for b right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.02916/b^2 = 1 how do I simplify?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1it will cross the y axis at + and  b

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1multiply by b^2, then take square root

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1should just say 54^2 = b^2 , so b is 54

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh lol, which beans I get +54?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok and then I plug that back in with the point 8,18 right?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1yep, they really gave you that value, but it checks correct

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1need to find + and  a, where it crosses x axis

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1use the other point, and the b value, solve a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.08^2/a^2 + 18^2/54^2 = 1 64/a^2 + 324/2916= 1 how do I simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got a = 6 * sqrt(2) Is that right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so I get: x^2/72 + y^2/2916 = 1 for the final equation is that right?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1when you have \[\frac{ 18^2 }{ 54^2 } = [\frac{ 18 }{ 54 }]^2\] reduce the inner fraction first, then square it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is my final equation correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x^2/72 + y^2/2916 = 1?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1yes that is right for a, but remember it is + and 

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so how do I change the final equation?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1for the standard form, you want to leave those denominators as a^2 and b^2, not expanded out

DanJS
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{ x^2 }{ [6\sqrt{2}]^2 }+\frac{ y^2 }{ 54^2 } = 1\]
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