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
- ap = rp'
- rp = ap'
- ap = rp' + 1
- ap'+ rp = 1
Hint:
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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