1.

Let the circles C1: x2+y2=9 and C2: (x−3)2+(y−4)2=16, intersect at the points X and Y. Suppose that another circle C3: (x−h)2+(y−k)2=r2 satisfies the following conditions: (i) centre of C3 is collinear with the centres of C1 and C2.(ii)C1 and C2 both lie inside C3, and(iii) C3 touches C1 at M and C2 at NLet the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be the tangent to the parabola x2=8αy.There are some expressions given in List−I whose values are given in List−II below:List IList II(I)2h+k (P) 6(II)length of ZWlength of XY (Q) √6(III)Area of triangle MZNArea of triangle ZMW (R) 54(IV)α (S) 215(T) 2√6(U) 103Which of the following is the only CORRECT combination?

Answer»

Let the circles C1: x2+y2=9 and C2: (x−3)2+(y−4)2=16, intersect at the points X and Y. Suppose that another circle C3: (x−h)2+(y−k)2=r2 satisfies the following conditions:



(i) centre of C3 is collinear with the centres of C1 and C2.



(ii)C1 and C2 both lie inside C3, and



(iii) C3 touches C1 at M and C2 at N



Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be the tangent to the parabola x2=8αy.

There are some expressions given in List−I whose values are given in List−II below:



List IList II(I)2h+k (P) 6(II)length of ZWlength of XY (Q) √6(III)Area of triangle MZNArea of triangle ZMW (R) 54(IV)α (S) 215(T) 2√6(U) 103

Which of the following is the only CORRECT combination?


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