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Q.

Statement-I : The distance of the normal to x2+2y2=5 at (1, 2) from origin is 132
Statement-II : The product of the perpendiculars from the foci of the ellipse x27+y24=1 to any tangent is 7
Statement-III: The distance between the foci of x225+y236=1 is 211

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a

both I & III 
 

b

both II & III 
 

c

both I & II 
 

d

neither I nor II 
 

answer is A.

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Detailed Solution

(I)

equation of ellipse x25+y252=1

equation of normal

5x1-52y2=5-52 5x-5y22=52 22 x-y=2

distance from (0, 0) is

28+1=23

 

(II) Product of perpendiculars from foci to any tangent to the ellipse is b2=4

(III) Distance between 

foci=2be         =236-25         =211 

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