If the circles `x^2+y^2+2x+2ky+6=0` and `x^2+y^2+2ky+k=0` intersect orthogonally then k equals (A) `2 or -3/2` (B) `-2 or -3/2` (C) `2 or 3/2` (D) `-2 or 3/2`

Options

A. `2 or -3//2`
B. `-2 or -3//2`
C. `2 or 3//2`
D. `-2 or 3//2`

Answer

A

Explanation

Since, circles cut orthogonally, if
`2g g'+2 f f'=c+c'`
`implies0+2k^(2)=6+k`
`implies2k^(2)-k-6=0`
`implies (2k +3)(k-2)=0`
`impliesk=2 or -3//2`