posted by .

A railroad tunnel is shaped like semi-ellipse. The height of the tunnel at the center is 69 ft and the vertical clearance must be 23 ft at a point 16ft from the center. Find an equation for the ellipse.

  • Trig -

    b = 69, a is unknown, and the point (16,23) is on it
    let the equation be
    x^2/a^2 + y^2/69^2 = 1
    16^2/a^2 + 23^2/69^2 = 1
    256/a^2 = 1 - 529/4761
    256/a^2 = 8/9
    8a^2 = 2304
    a^2 = 288

    x^2/288 + y^2/4761 = 1

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. alg

    identify the conic section. if its a parabols give the vertex if its a circle, give the center and radius. if it is an ellipse or a hyperbola, give the center and foci. again my teacher said the answer is ellipse with center (-4,4), …
  2. Calc

    Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at …
  3. physics

    The angular momentum of a planet is conserved if taken with respect to: a)The center of the ellipse b) The focus of the ellipse at the sun c)The focus of the ellipse opposite the sun d)Both foci of the ellipse
  4. Trig

    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 …
  5. Precalculus Trig (Geometry)

    A rectangular doorway is 38 meters wide and 60 meters high. The doorway is capped with a semi-ellipse that is 13 meters high at its center. Find the height h of the doorway and window 5 meters from the center. From the ellipse equation, …
  6. math

    find equation of the ellipse whose center is at the origin and foci f(2,2) f(-2,-2) and length of semi-major axis is square root of 8?
  7. math

    The roof of a tunnel is in the shape of a parabolic arch whose highest point is 18m above the road. The road surface is 16m wide. Lights are placed in the tunnel 12 meters high. How far from center of the tunnel are the lights placed?
  8. Algebra

    The arch of the bridge below is half an ellipse, a "semi-ellipse". The arch is 148m long and has a height of 48m at the center. The height of the arch is 10m at point p. What is the distance from p to the center?
  9. math

    A railroad tunnel is shaped like a semi-eclipse. The height of the tunnel is 28ft and the total width is 50ft. Find the vertical clearance at a point 13ft to the right from the center. Please show all work that leads to your answer. …
  10. Math

    Write the equation of the ellipse using the given information: The axis has lengths 2 and 5; the major axis is vertical; and the center of the ellipse is (–1, –2).

More Similar Questions