Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length `2sqrt7` on y-axis is (are)

Options

A. `x^(2)+y^(2)+6x+8y+9=0`
B. `x^(2)+y^(2)+6x+7y+9=0`
C. `x^(2)+y^(2)+6x-8y+9=0`
D. `x^(2)+y^(2)+6x-7y+9=0`

Answer

C

Explanation

Here, length of intercept on Y-axis `=2sqrt(f^(2)-c)` and if circle touches X-axis `rArr g^(2)=c,for x^(2)+y^(2)+2gx+2fy+c=0` passes through (3,0).`
` and `2sqrt(f^2-c=2sqrt7) rArr f^(2)-c=7` from egs. (i) and (ii). `g^(2)+6g+9=0rArr(g+3)^(2)=0`
`thereforeg=-3and c=9`
`therefore f^(2)=7+c=16`
`rArr f=+-4`
`thereforex^(2)+y^(2)-6x+-8y+9=0`