If the line l x+m y+n=0 cuts the ellipse x^2 a^2 + y^2 25 =1 in points whose eccentoric angles differ by 2 , then a^2 l^2+b^2 m^2 n^2 is equal to

Step-by-step solution

Let the points of intersection of the line and the ellipse be (a , b ) and a ( 2 + ), b ( 2 + ) , since they lie on the given line l x+m y+n=0 . l a +m b +n=0 l a +m b =-n and l a +m b +n=0l a -m b =n squarring and adding, we get, a^2 l^2+b^2 m^2=2 n^2 a^2 l^2+b^2 m^2 n^2 =2 .