Question
If P is a point on the ellipse of eccentricity e and A, A' are the vertices and S, S' are the focii then ΔSPS' : ΔAPA'=
- e3
- e2
- e
- 1/e
Hint:
assume the height of the triangles to be some variable , say h since both the triangles have the same height.
The correct answer is: e
e
Let the length of perpendicular from the point P to the major axis be h
Area of triangle A’PA = 2ah/2= ah
Area of triangle S’PS = 2aeh/2= aeh
Therefore, SPS’: APA’ = aeh: ah = e
calculate the areas of the triangles in terms of the parameters of the ellipse and calculate the raio.
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