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Q: P is point on the ellipse x^2/a^2 + y^2/b^2 = 1 with foci at S, S'. Normal at P cuts the x-axis at G and if SP/SP' = 2/3 then SG/SG' = 

Solution:

Foci of the ellipse are (ae, 0) and (-ae, 0).

Let S = (ae, 0) and S' = (-ae, 0)

Let be any point on the ellipse.

Given: SP/S'P = 2/3

Equation of normal at P is

It meets x-axis at