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Question : 54
Total: 54
Answer the following by appropriately matching the lists based on the information given in the paragraph.
Let the circlesC 1 : x 2 + y 2 = 9 and C 2 : ( x − 3 ) 2 + ( y − 4 ) 2 = 16 intersect at the points X and Y. Suppose that another circle C 3 : ( x − h ) 2 + ( y − k ) 2 = r 2 satisfies thefollowing conditions :
(i) Centre ofC 3 is collinear with the centres of C 1 and C 2
(ii)C 1 and C 2 both lie inside C 3 , and
(iii)C 3 touches C 1 at M and C 2 at N
Let the line through X and Y intersectC 3 at Z and W, and let a common tangent of C 1 and C 3 be a tangent to the parabola x 2 = 8 α y
There are some expressions given in the List – I whose values are given in List – II below
Which of the following is the only CORRECT combination?
Let the circles
(i) Centre of
(ii)
(iii)
Let the line through X and Y intersect
There are some expressions given in the List – I whose values are given in List – II below
List I | List II | ||||
---|---|---|---|---|---|
I) | P) 6 | ||||
II) | Q) | ||||
III) | R) | ||||
IV) α | S) | ||||
T) | |||||
U) |
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