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Tangent to ellipse also tangent to circle

  1. Jan 28, 2015 #1
    1. The problem statement, all variables and given/known data
    if the tangent at a point P("theta") on the ellipse
    16 (x^2) + 11 (y^2) = 256​
    is also tangent to the circle
    (x^2) + (y^2) + 2(x) = 15​
    then ("theta") = ??

    2. The attempt at a solution

    {{{{ i have taken "theta" as "d" }}}}​

    P [4 cos d , (16/(sqrt11)) sin d]

    equation of tangent at P on ellipse is {(cos d) / 4] x + [(sin d) / (16/(sqrt11))] y = 1 .....................(i)

    centre of given circle C(-1,0) and radius r = 4

    for (i) to also be tangent on the circle - perpendicular distance of (i) from C must be equal to 4

    but when i tried to do so i could not get the answer
    may be I am doing something wrong so please anyone could guide me the correct way
     
  2. jcsd
  3. Jan 28, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    The approach looks good, so please show your work so we can see what went wrong.
     
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