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Answer the following by appropriately matching the lists based on the information given in the paragraph
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 a tangent to the parabola x2 = 8αy.
There are some expression given in the List-I whose values are given in List-II below:

Which of the following is the only CORRECT combination?
  • a)
    (II), (T)
  • b)
    (I), (S)
  • c)
    (I), (U)
  • d)
    (II), (Q)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Answer the following by appropriately matching the lists based on the ...

MC1 + C1C2 + C2N =  2r
⇒ 3 + 5 + 4 = 2r ⇒ r = 6 ⇒ Radius of C3 = 6
Suppose centre of C3 be  

Equation of ZW and XY is  3x + 4y – 9 = 0
(common chord of circle C1 = 0 and C2 = 0)


Let length of perpendicular from M to ZW be 

C1 : x2 + y2 – 9 = 0
common tangent to C1 and C3 is common chord of C1 and C3 is 3x + 4y + 15 = 0.
Now 3x + 4y + 15 = 0 is tangent to parabola x2 = 8αy.

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Answer the following by appropriately matching the lists based on the information given in theparagraphLet 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 bea tangent to the parabola x2 = 8αy.There are some expression given in the List-I whose values are given in List-II below:Which of the following is the only CORRECT combination?a)(II), (T)b)(I), (S)c)(I), (U)d)(II), (Q)Correct answer is option 'D'. Can you explain this answer?
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Answer the following by appropriately matching the lists based on the information given in theparagraphLet 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 bea tangent to the parabola x2 = 8αy.There are some expression given in the List-I whose values are given in List-II below:Which of the following is the only CORRECT combination?a)(II), (T)b)(I), (S)c)(I), (U)d)(II), (Q)Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Answer the following by appropriately matching the lists based on the information given in theparagraphLet 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 bea tangent to the parabola x2 = 8αy.There are some expression given in the List-I whose values are given in List-II below:Which of the following is the only CORRECT combination?a)(II), (T)b)(I), (S)c)(I), (U)d)(II), (Q)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Answer the following by appropriately matching the lists based on the information given in theparagraphLet 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 bea tangent to the parabola x2 = 8αy.There are some expression given in the List-I whose values are given in List-II below:Which of the following is the only CORRECT combination?a)(II), (T)b)(I), (S)c)(I), (U)d)(II), (Q)Correct answer is option 'D'. Can you explain this answer?.
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