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The set of values of k, for which the circle C : 4x2 + 4y2 – 12x + 8y + k = 0 lies inside the fourth quadrant and the point ( 1 , − 1 3 )  lies on or inside the circle C, is

Option 1 -

 an empty set

Option 2 -

( 6 , 6 5 9 ]

Option 3 -

[ 8 0 9 , 1 0 )

Option 4 -

( 9 , 9 2 9 ]

0 5 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • P

    Answered by

    Payal Gupta | Contributor-Level 10

    2 months ago
    Correct Option - 4


    Detailed Solution:

    C : 4x2 + 4y2 – 12x + 8y + k = 0

    ? ( 1 , − 1 3 )               

    Lies on or inside the C then

    4 + 4 9 − 1 2 − 8 3 + k ≤ 0

    ⇒ k ≤ 9 2 9               

    Now, circle lies in 4th quadrant centre

    ≡ ( 3 2 , − 1 )               

    ∴ r < 1 ⇒ 9 4 + 1 − k 4 < 1               

    ⇒ 1 3 4 − k 4 < 1

    ⇒ k 4 > 9 4

    ⇒ k > 9

    ∴ K ∈ ( 9 , 9 2 9 )      

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