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Q.

Statement-I : The sum of the slopes of the tangents drawn from (5,4) to x216+y212=1 is 409

Statement-II :The product of the slopes in the above situation is 49

Which of the above statements is true

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a

neither I nor II

b

both I & II

c

only II

d

only I

answer is C.

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Detailed Solution

(I)

Given ellipse x216+y212=1 where a2=16,b2=12  and the point=(5,4) Now m1+m2=2x1y1x12-a2              =2×5×425-16              =409

(II)

m1m2=y12-b2x12-a2           =16-1225-16           =49

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Statement-I : The sum of the slopes of the tangents drawn from (5,4) to x216+y212=1 is 409Statement-II :The product of the slopes in the above situation is 49Which of the above statements is true