The point of contact of the circle `x^(2)+y^(2)+2x+2y+1=0 and x^(2)+y^(2)-2x+2y+1=0`

Options

A. (0,1)
B. (0,-1)
C. (1,0)
D. (-1,0)

Answer

B

Explanation

Given circles are, `x^(2) + y^(2) + 2x +2y + 1 = 0`
and `x^(2) + y^(2) - 2x + 2y + 1 = 0`
`implies C_(1) = (-1,1)` and `C_(2) = (1,-1)`
`r_(1) = sqrt(1 + 1 - 1) = 1` and `r_(2) = sqrt(1 + 1 - 1) = 1`
`C_(1)C_(2) = sqrt(2^(2) + 0) = 2, r_(1) + r_(2) = 1 + 1 = 2`
`implies C_(1)C_(2) = r_(1 ) + r_(2)` and `r_(1) = r_(2)`
`:.` Point of contact = Mid point of `C_(1) C_(2) = (0, -1)`