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Let the circle C(1):x^(2)+y^(2)=9 and C(...

Let the circle `C_(1):x^(2)+y^(2)=9` and `C_(2):(x-3)^(2)+(y-4)^(2)=16` intersect at the point X and Y. Suppose that another circle `C_(3):(x-h)^(2)+(y-k)^(2)=r^(2)` satisfies the following conditions
(i). Centre of `C_(3)` is collinear with the center of `C_(1)&C_(2)`
(ii). `C_(1)&C_(2)` both lie inside `C_(3)` and
(iii). `C_(3)` touches `C_(1)` at M and `C_(2)` at N
Let hte line through X and Y intersect `C_(3)` at Z and W and let a common tangent of `C_(1)` & `C_(3)` be a tangent to the parabola `x^(2)=8alphay`
There are some expressions given in the following lists
`{:("List I","List II"),((I)" "2h+k,(P)" "6),((II)" "("length of ZW")/("length of XY"),(Q)" "sqrt(6)),((III)" "("Area of "DeltaMZN)/("Area of "DeltaZMW),(R)" "(5)/(4)),((IV)" "alpha,(S)" "(21)/(5)),(,(T)" "2sqrt(6)),(,(U)" "(10)/(3)):}`
Q. Which of the following is the only correct combination?
(A) (I)-(S)
(B) (II)-(Q) ltBrgt (C) (I)-(U)
(D) (II)-(T)

A

(II), (T )

B

(I), (S)

C

(I ) , (U )

D

(II) , ( Q)

Text Solution

Verified by Experts

The correct Answer is:
D
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