Question
If F1 and F2 are the feet of the perpendiculars from the foci S1 & S2 of an ellipse on the tangent at any point P on the ellipse, then (S1 F1). (S2 F2) is equal to-
- 2
- 3
- 4
- 5
Hint:
find out the values of a,b and e from the equation. assume a point on the ellipse and find out the values of required distances.
The correct answer is: 3
3
a= √5
b= √3
e= √(1-3/5) = √(2/5)
let’s assume the point p to be at the end of the major axis.
in this case,
S1F1 = a-ae
S2F2= a+ae
(a-ae)(a+ae) = a2-a2e2 = 5-5(2/5)
3
selecting a point on the major axis provides an ease of calculation.
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