JEE Main20252 Apr 2025Morning ShiftMathematicsEllipseActual

If S and S^ are the foci of the ellipse x^2 18 + y^2 9 =1 and P be a point on the ellipse, then (S P . S^ P )+ ( SP . S ^ P ) is equal to :

Options

A3(1+ 2 )
B3(6+ 2 )
C9
D27

Correct answer

D. 27

Step-by-step solution

PS + PS ^ =2 3 2 b ^2= a ^2 (1- e ^2 ) 9=18 (1- e ^2 ) e = 1 2 Directrix x = a e = 3 2 1 2 =6 P S P S '= | 1 2 (3 2 -6) 1 2 (3 2 +6) | = 1 2 |18 ^2 -36 | ( PS PS ^ )_ =18 ;( PS PS )_ =9 sum =27

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