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Find the angle between the circles given...

Find the angle between the circles given by the equations.
`x^2 + y^2 - 12x - 6y + 41 = 0,`
` x^2 + y^2 + 4x + 6y - 59 = 0.`

Text Solution

Verified by Experts

The correct Answer is:
`theta=pi/4`
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Find the angle between the circles given by the equations. x^2 + y^2 + 6x - 10y - 135 = 0, x^2 + y^2 - 4x - 116 = 0

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Knowledge Check

  • The equation of the tangent at the point (0,3) on the circle which cuts the circles x^2 + y^2 -2x + 6y =0, x^2 + y^2 - 4x -2y + 6 =0 and x^2 + y^2 -12x +2y + 3 =0 orthogonally is

    A
    `y=3`
    B
    `x=0`
    C
    `3x+y -3=0`
    D
    `x+3y-9=0`

  • 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

    • Similar Questions

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    If the angle between the circles x^2 + y^2 - 12x - 6y + 41 = 0 and x^2 + y^2 + kx + 6y - 59 = 0 is 45^@ find k.

    Find k if the following pairs of circles are orthogonal. x^2 + y^2 - 6x - 8y + 12 = 0 , x^2 + y^2 - 4x + 6y + k = 0

    Find the equation of the radical axis of the following circles. x^2 + y^2 -2x - 4y -1 = 0. x^2 + y^2 - 4x - 6y + 5 = 0 .

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    Find the equation of the radical axis of the following circles. x^2 + y^2 + 4x + 6y -7 = 0. 4(x^2 + y^2) + 8x + 12y - 9 = 0.

    Find the external centre of similitude for the circles x^(2) + y^(2) - 2x - 6y + 9 =0 and x^(2) + y^(2) = 4

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