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Prove that the radii of circles x^2 + y^...

Prove that the radii of circles `x^2 + y^2 = 1, x^2 + y^2 - 2x -6y = 6` and `x^2 + y^2 - 4x - 12y = 9` are in A.p.

Answer

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Prove that the centres of the three circles x^(2) + y^(2) - 2x + 6y + 1 = 0, x^(2) + y^(2) + 4x - 12y + 9 = 0 and x^(2) + y^(2) - 16 = 0 are collinear.

Show that the centres of the following circles lie on a line and their radii are in A.P. : x^(2) + y^(2) = 1, x^(2) + y^(2) + 6x - 2y -6 = 0, x^(2) + y^(2) - 12x + 4y - 9 = 0 .

Knowledge Check

  • The circle x^2 + y^2 - 2x - 4y + 1 = 0 and x^2 + y^2 + 4x + 4y - 1 = 0

    A
    touches internally
    B
    touch externally
    C
    have 3x + 4y - 1 = 0 the common tangent at the point of contact
    D
    have 3x + 4y + 1 = 0 as the common tangent at the point of contact

  • Center of the circle x^(2) + y^(2) - 4x + 6y - 12 = 0 is -

    A
    (2, 3)
    B
    (2, -3)
    C
    (-2, 3)
    D
    (-2, -3)

    • Similar Questions

    Explore conceptually related problems

    Prove that the centres of the circles x^(2) + y^(2) - 10x + 9 = 0, x^(2) + y^(2) - 6x + 2y + 1 = 0 and x^(2) + y^(2) - 18x - 4y + 21 = 0 lie on a line, find the equation of the line on which they lie.

    Find the equation to the common chord of the two circles x^(2) + y^(2) - 4x + 6y - 36 = 0 and x^(2) + y^(2) - 5x + 8y - 43 = 0 .

    A circle through the common points of the circles x^(2) + y^(2) - 2x - 4y + 1 = 0 and x^(2) + y^(2) - 2x - 6y + 1 = 0 has its centre on the line 4x - 7y - 19 = 0 . Find the centre and radius of the circle .

    Center of the circle x^(2) + y^(2) - 6x + 4y - 12 = 0 is -

    Show that the circles x^(2) + y^(2) + 6x + 2y + 8 = 0 and x^(2) + y^(2) + 2x + 6y + 1 = 0 intersect each other.

    Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

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