Question

The length of the tangent of the ellipse `x^2/25+y^2/16=1` intercepted between auxiliary circle such that the portionof the tangent intercepted between the auxiliary circle subtends equal angles at foci is
A. 6
B. 3
C. 4
D. 8

Answer 1

Let AB be the length of the tangent intercepted by auxiliary circle and `S_(1),S_(2)` be the foci.
Given that
`angleAS_(1)B=angleAS_(2)B`
`rArrangleS_(1)AB=angleS_(2)AB=(pi)/(2)`
So `AS_(1)S_(2)B` is a rectangle.
`:. AB=S_(1)S_(2)=2aex=2xx5xx(3)/(5)=6`