Match the column:
Column-I | Column-II |
(i) If the mid point of a chord of the ellipse= 1 is (0, 3), then length of the chord is then k is | [A] 6 |
(ii) If the line y = x + λ touches the ellipse 9x2 + 16y2 = 144, then the sum of values of λ is | [Β] 8 |
(iii) If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be , then length of the minor axis is , then k is | [C] 0 |
(iv) Sum of distances of a point on the ellipse = 1 from the foci | [D]16 |
[E] 7 |
Text Solution
Verified by Experts(i) [B]; (ii)[C]; (iii)[D]; (iv)[B]
Ans.
(i) [B]
(ii)[C]
(iii)[D]
(iv)[B]
Sol.
(i) Equation of the chord whose mid point is (0, 3) is
– 1 = 
– 1 i.e. y = 3
if intersects the ellipse 
= 1
at 
⇒ x = ± 
∴ length of the chord = 
thus 
∴ k = 8
(ii) If the line y = x + λ touches the ellipse 9x 2 + 16y 2 = 144 then λ 2 = 16(1) 2 + 9 ⇒ λ = ± 5
(iii) 
– ae = 8 ⇒ 2a – 
= 8 i.e. a = 
b 2 = a 2 (1 – e 2 ) = 
∴ length of minor axis = 2b = 
∴ k = 16
(iv) Sum of the distance of a point on the ellipse from the focii = 2a = 8
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