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If the radical axis of the circles x^2+y...

If the radical axis of the circles `x^2+y^2+2gx+2fy+c=0` and `2x^2+2y^2+3x+8y+2c=0` touches the circle `x^2+y^2+2x+1=0` , show that either `g=3/4` or `f=2`

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If the radical axis of the circles x^2 + y^2 + 2gx + 2fy + c = 0 and 2x^2 + 2y^2 + 3x + 8y+2c=0 touches the circle x^2 + y^2 + 2x - 2y + 1 = 0 , show that either g= 3/4 or f = 2 .

The radical axis of the circles x^(2)+y^(2)+2gx+c=0 and 2x^(2)+2y^(2)+3x+2y+2c=0 touches the circle x^(2)+y^(2)+y^(2)+2x+2y+1=0 if

Knowledge Check

  • If the radical axis of the circles x^(2)+y^(2) +2gx +2fy+c=0 and 2x^(2)+2y^(2)+3x+8y+2c=0 touches the circle x^(2)+y^(2)+2x+2y+1=0 , then

    A
    `g=3//4 and f ne 2`
    B
    `g ne 3//4 and f =2`
    C
    `g=3//4 or f =2`
    D
    none of these

  • The radical centre of the circles x^2+y^2+2gx+2fy+c=0 and 2x^2+2y^2+3x+8y+2c=0 , touches the circle x^2+y^2+2x+2y+1=0 , then

    A
    g=3/4 and `f ne 2`
    B
    `g ne 3/4` and f=2
    C
    g=3/4 and f = 2
    D
    None of these

  • Circles x^(2)+y^(2) - 2x - 4y=0 and x^(2)+y^(2)-8y-4=0

    A
    touch externally
    B
    touch internally
    C
    do not touch
    D
    none

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