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Math Help - Ellipse problem

  1. #1
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    Sep 2008
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    Ellipse problem

    Q)If the normal at the end of the latus rectum of an ellipse
    x^2/a^2 + y^2/b^2=1

    passes through one extemity of minor axis ,then the eccentricity of ellipse is given by ?

    a)e^4+e^2+1=0

    b)e^4+e^3+e^2+e +1=a

    c)e^4+e^2-1=0

    d)none of the above

    Thanks in advance guys .
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  2. #2
    Super Member
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    Hi sid 178, welcome to PF.
    The co-ordinates of the one end of the latus rectum is ( ae, b^2/a).
    The slope of the tangent at that point is given by
    2x/a^2 + 2yy'/b^2 = 0
    y' = [-x1b^2/y1a^2]. Substitute the values of (x1, y1). You get
    y' = .......?
    Find the slope of the normal. The end point of the minor axis is ( 0, -b).
    m = [b^2/a + b]/ae.
    Since tangent and normal are perpendicular to each other
    m*y' = -1.
    Simplify the result by using the relation b^2 = a^2( 1 - e^2).

    Answer: e^4 + e^2 - 1 = 0
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