Let the circle (x – 1) 2 + (y – 1) 2 = 25 cuts a rectangular hyperbola with transverse axis along the line y = x at four points A, B, C, D having co-ordinates (x i , y i ), i = 1, 2, 3, 4 respectively, O being the centre of the hyperbola. Match the following columns
Column-I | Column-II |
(i) x1 + x2 + x3 + x4 is equal to | [A] 2 |
(ii) is equal to | [B] 44 |
(iii) OA2 + OB2 + OC2 + OD2 is equal to | [C] 50 |
(iv) is equal to | [D]100 |
[E]20 |
Text Solution
Verified by Experts(i) [A]; (ii) [C]; (iii) [D]; (iv) [C]
Ans.
(i) [A]
(ii) [C]
(iii) [D]
(iv) [C]
Sol.
Let the equation of hyperbola xy = c 2
solving hyperbola & circle
x 4 – 2x 3 –23x 2 –2xc 2 + c 4 = 0
so x 1 + x 2 + x 3 + x 4 = 2
= (x 1 + x 2 +x 3 +x 4 ) 2 – 2 
= 4 – 2 (–23) = 50
x = 
so equation becomes
y 4 – 2y 3 –23y 2 –2c 2 y + c 4 = 0
so 
= 50
So, 
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