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The circles whose equations are x^2+y^2+...

The circles whose equations are `x^2+y^2+c^2=2ax` and `x^2+y^2+c^2-2by=0` will touch one another externally, if :

A

`1/b^2+1/c^2=1/a^2`

B

`1/c^2+1/a^2=1/b^2`

C

`1/a^2+1/b^2=1/c^2`

D

`1/b^2+1/c^2=2/a^2`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • The two circles x^2+y^2=ax and x^2+y^2=c^2 (cgt0) touch each other if

    A
    `|a|=c`
    B
    a = 2c
    C
    `|a|=2c`
    D
    `2|a|=c`

  • If the circles x ^(2) +y^(2) +2gx +2fy =0 and x ^(2) +y^(2) +2g'x+ 2f'y=0 touch each other then-

    A
    `f f' =g g'`
    B
    `fg=f'g'`
    C
    `f^(2)g =f' g'`
    D
    `f g' =gf'`

  • If one of the circles x^2+y^2+2ax+c=0 and x^2+y^2+2bx+c=0 lies within the other, then :

    A
    `abgt0`, `cgt0`
    B
    `abgt0`, `clt0`
    C
    `ablt0`, `cgt0`
    D
    `ablt0`, `clt0`

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