Consider circles
`C_(1): x^(2) +y^(2) +2x - 2y +p = 0`
`C_(2): x^(2) +y^(2) - 2x +2y - p = 0`
`C_(3): x^(2) +y^(2) = p^(2)`
Statement-I: If the circle `C_(3)` intersects `C_(1)` orthogonally then `C_(2)` does not represent a circle
Statement-II: If the circle `C_(3)` intersects `C_(2)` orthogonally then `C_(2)` and `C_(3)` have equal radii Then which of the following is true?

Options

A. statement II is false and statement I is true
B. statement I is false and statement II is true
C. both the statements are false
D. both the statements are true

Answer

B

Explanation

If `C_(3)` and `C_(1)` intersect orthogonally then `p =p^(2) =0`
`rArr p =1, 0 rArr C_(2)` represents a circle
`rArr` statement I is false
If `C_(3)` and `C_(2)` intersect orthogonally then `p =- 1`
`rArr` for this 'p' `C_(2)` and `C_(3)` have equal radii.
`rArr` statement -II is correct