The locus of a point whose chord of contact with respect to the ellipse x2+2y2=1 subtends a right angle at the centre of the ellipse is

Dear Student,

Please find below the solution to the asked query :
ellipse is x^2+ 2y^2 = 1 ---------------------------------------(... 
let (h,k,) is moving point  
equation to the chord of contact is ;-- 
hx + 2ky =1--------------------------(II) 
to get theequation of line joining the center (0.0 ) of the ellipse to 
the point of intersection of (I) 7 (II) make (I) homogeneous with 
the help of (II) 
x^2 + 2y^2 = ( hx+ 2ky)^2 
or x^2 + 2y^2= h^2x^2+ 4hkxy+ 4k^2y^2 
x^2[ 1- h^2) + y^2[ 2- 4k^2) - 4hkxy =0 
the lines are at right angle if --- 
coefficient of x^2+ coefficient of Y^2 = 0 
1- h^2 + 2- 4k^2 = 0 
or h^2 + 4k^2 = 3 
so locus of (h,k ) is ;--[putting h=x & k=y ] 
x^2 + 4y^2 = 3

Hope this would clear your doubt about the topic.

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