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Orthogonality OF two circles...

Orthogonality OF two circles

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Knowledge Check

  • If centre of a circle lies on the line 2x - 6y + 9 =0 and it cuts the circle x^(2) + y^(2) = 2 orthogonally then the circle passes through two fixed points

    A
    `((1)/(2),(3)/(2)),((-2)/(5),(6)/(5))`
    B
    `(2, 3), (-2, 6)`
    C
    `((-1)/(2), (3)/(2)),((-2)/(5),(6)/(5))`
    D
    `(-2, 3)(-2, 6)`

  • The centre of circle S lies on 2x - 2y +9=0 and it cuts orthogonally the circle x^(2)+y^(2)=4 . Then the circle passes through two fixed points

    A
    (1, 1), (3, 3)
    B
    `(-1//2,1//2), (-4, 4)`
    C
    (0, 0), (5, 5)
    D
    none

  • The locus of centre of circle passing through (a, b) and cuts orthogonally the circle x^(2)+y^(2)=p^(2) is

    A
    `2ax+2by-(a^(2)+b^(2)+p^(2))=0`
    B
    `2ax+2by-(a^(2)-b^(2)+p^(2))=0`
    C
    `x^(2)+y^(2)-3ax-4by +(a^(2)+b^(2)-p^(2))=0`
    D
    `x^(2)+y^(2)-2ax+3by+(a^(2)-b^(2)+p^(2))=0`

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