Maths-
General
Easy

Question

If p and p' denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length a, respectively, on a tangent to the ellipse and r denotes the focal distance of the point, then

  1. ap = rp'    
  2. rp = ap'    
  3. ap = rp' + 1    
  4. ap'+ rp = 1    

hintHint:

find out the equation of tangent to the ellipse. find out the values of p and p'.

The correct answer is: ap = rp'



    rp’=ap
    equation of tangent  of the ellipse: (x cos t)/a + (y sin t)/b-1=0
    let z = √(cos 2t /a2+ sin2t /b2)
    length of perpendicular from the focus (ae,0) : p = (ecos t -1)/z
    distance from the center p’ = 1/z

    given, r = aecos t – a

    rp’ = a(ecos t – 1)/z
    ap = a(ecos t -1)/z
    hence, rp’=ap

    the distances of the points from a line can be calculated by using the distance formula.

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