Match the column:
Column-IColumn-II(i) For a rectangular hyperbola xy = c2 (c is purely imaginary) …

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Match the column:
Column-IColumn-II(i) For a rectangular hyperbola xy = c2 (c is purely imaginary) if a point on it is (a, α) where 'a' is a positive number, α can take value[A] 3(ii) If sides of a triangle are in A.P. and (a – b + c) s = kb2 (where s is the semi perimeter) then k is equal to[B] (iii) Radius of the circle having centre (3, 4) and touching the circle x2 + y2 = 4 can be[C]17(iv) Maximum distance of any point on the circle (x – 7)2 + (y – 2)2 = 16 from the centre of the ellipse 25x2 + 16y2 = 400 is[D]

CGP EDU Academic Team · Accepted Answer

The correct answer is (i) [B]; (ii) [D]; (iii) [A]; (iv) [C]. Ans.
(i) [B]
(ii) [D]
(iii) [A]
(iv) [C]
Sol.
(i) xy = c 2 = –ive (  c is purely imaginary)
⇒ if x is positive y must be negative real ⇒ 
(ii) 2b = a + c
Now, (a + c – b) s = kb 2 ⇒  = kb
2 ⇒  = kb 2 ⇒ k = 
(iii) r =  – 2 = 3
(iv) 17

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Column-I	Column-II
(i) For a rectangular hyperbola xy = c2 (c is purely imaginary) if a point on it is (a, α) where 'a' is a positive number, α can take value	[A] 3
(ii) If sides of a triangle are in A.P. and (a – b + c) s = kb2 (where s is the semi perimeter) then k is equal to	[B]
(iii) Radius of the circle having centre (3, 4) and touching the circle x2 + y2 = 4 can be	[C]17
(iv) Maximum distance of any point on the circle (x – 7)2 + (y – 2)2 = 16 from the centre of the ellipse 25x2 + 16y2 = 400 is	[D]

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