A line through P( λ , 3) meets the ellipse 
+ 
= 1 at A and D meets the x-axis and y-axis at B and C respectively, so that PA.PD = PB.PC, then | λ | is greater than or equal to ………….
Text Solution
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Ans. 0008
Sol. Let the equation of line through P( λ , 3) be
= r ⇒ x = λ + r cos θ and y = 3 + r sin θ
Line meets the ellipse 
Such that 9x 2 + 16y 2 = 144 at A and D
⇒ 9( λ + r cos θ ) 2 + 16(3 + r sin θ ) 2 = 144
⇒ 9( λ 2 + r 2 cos 2 θ + 2 λ r cos θ ) + 16 (9 + r 2 sin 2 θ + 6r sin θ )
= 144
⇒ (9cos 2 θ + 16 sin 2 θ ) r 2 +
(18 λ cos θ + 96 sin θ )r + 9 λ 2 = 0
∴ PA.PD = 
… (i)
Since line meet the axes at B and C
So, PB.PC = 
…. (ii)
from (i) & (ii)
λ ≥ 8
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