A) \( \Large 2\ or\ -\frac{3}{2} \) |
B) \( \Large -2\ or\ \frac{3}{2} \) |
C) \( \Large 2\ or\ \frac{3}{2} \) |
D) \( \Large -2\ or\ -\frac{3}{2} \) |
A) \( \Large 2\ or\ -\frac{3}{2} \) |
Given equations of circles are \( \Large x^{2}+y^{2}+2x+2ky+6=0\ and\ x^{2}+y^{2}+2ky+k=0 \). They intersect each other orthogonally
\( \Large 2gg' + 2ff = c+c \)
=> \( \Large 2.1.0 + 2.k.k = 6 + k \)
=> \( \Large 2k^{2}-k-6=0 \)
=> \( \Large \left(2k+3\right) \left(k-2\right)=0 \)
=> \( \Large k = 2,\ -\frac{3}{2} \)