If two points are taken on the minor axis of an ellipse at the same distance from the center as the foci, then the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is -
Text Solution
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Let the equation of the ellipse be
Then, the distance of a focus from the centre = ae
= a 
= 
So that the two points on the minor axis are
S 1 (0, 
) and S 1 ′ (0, – 
).
Now any tangent to the ellipse is
y = mx + 
, where m is aparameter.
The sum of the squares of the perpendiculars on this tangent from the two points
S 1 and S 1 ′ = 
+ 
= 
= 2a 2 (constant).
Hence is the correct answer.
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