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Find the value of k, if the circles x^(2...

Find the value of k, if the circles `x^(2) + y^(2) + 4x + 8 = 0` and `x^(2) + y^(2) - 16y + k = 0` are orthogonal.

Text Solution

Verified by Experts

The correct Answer is:
`= - 8`
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Find k if the cirlces x^(2)+y^(2)-5x-14y-34=0 and x^(2)+y^(2)+2x+4y+k=0 are orthogonal to each other.

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Knowledge Check

  • If the circles x^(2) + y^(2) - 6x - 8y + 12 = 0 , x^(2) + y^(2) - 4x + 6y + k = 0 cut orthogonally, then k =

    A
    `- 24 `
    B
    `24 `
    C
    12
    D
    15

  • The locus of the centre of the circle which cuts the circles x^(2) + y^(2) + 4x - 6y + 9 = 0 " and " x^(2) + y^(2) - 4x + 6y + 4 = 0 orthogonally is

    A
    ` 8x + 12y - 5= 0 `
    B
    `8x - 12y + 5 = 0 `
    C
    `4x - 6y + 5 = 0 `
    D
    none

  • The locus of centres of the circles which cut the circles x^(2) + y^(2) + 4x - 6y + 9 = and x^(2) + y^(2) - 5x + 4y + 2 = 0 orthogonally is

    A
    3x + 4y - 5 = 0
    B
    9x - 10y + 7 = 0
    C
    9x + 10y - 7 = 0
    D
    9x - 10y + 11 = 0

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