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Analytic geometry: ellipse

  1. May 21, 2012 #1
    1. The problem statement, all variables and given/known data
    .
    1. a hall that is 10 ft. wide has a ceiling that is a semi-ellipse. the ceiling is 10 ft high at the sides and 12 ft high in the center find its equation with the x axis horizontal and the origin at the center of the ellipse.

    2. Relevant equations

    x^2/a^2 + y^2/b^2 = 1


    3. The attempt at a solution

    The difference between the height at the ceiling and the sides is 12-10 = 2 ft. This is the value of b.

    I assume that the vertices of the ellipse are 10 feet apart, the same as the width of the hall. This means that the major axis is 10 ft. Therefore, a = 10/2 =5.

    The equation of the ellipse is x^2/25 + y^2/4 = 1

    p.s. i think i got the right answer but i need a better solution.

    1. The problem statement, all variables and given/known data

    the point p1(x1,y1) lies outside the circle whose center is at (h,k) and whose radius is r. if T is the length of the tangent from p1 to the circle, prove that t2=(x1-h)^2+y1-k)^2-r^2


    2. Relevant equations

    (x-h)^2+(y-k)^2=r^2


    3. The attempt at a solution

    P (x1,y1) (x-h)^2+(y-k)^2=r^2

    i used distance formula

    P (x1,y1) to (x-h)^2+(y-k)^2-r^2=0

    = (x1-h)^2+y1-k)^2-r^2
     
  2. jcsd
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