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If a variable line 3x+4y-lamda=0 is such...

If a variable line `3x+4y-lamda=0` is such that the two circles `x^(2)+y^(2)-2x-2y+1=0 " and" x^(2)+y^(2)-18x-2y+78=0` are on its opposite sides, then the set of all values of `lamda` is the interval

A

[12,21]

B

(2, 17)

C

(23, 31)

D

[13, 23]

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • If a variable line, 3x + 4y -lambda = 0 is such that the two circles x^(2)+y^(2)-2x-2y+1=0 and x^(2)+y^(2)-18x-2y+78=0 are not its opposite sides, then the set of all values of lambda is the interval

    A
    [13, 23]
    B
    [2,17]
    C
    [12,21]
    D
    [23,31]

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    B
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    one lies inside the other
    D
    each lies outside the other

  • The two circles x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-4x-6y-8=0 are such that

    A
    they touch each other
    B
    they intersect each other
    C
    one lies inside the other
    D
    each lies outside the other

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