A) \[\frac{-5}{2}\]
B) \[-1\]
C) \[\frac{-11}{8}\]
D) \[\frac{-5}{4}\]
Correct Answer: D
Solution :
If two circles \[{{x}^{2}}+{{y}^{2}}+2{{g}_{1}}x+2{{f}_{1}}y+{{c}_{1}}=0\] and \[2({{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}})={{c}_{1}}+{{c}_{2}}\] intersect orthogonally then they must follow \[2({{g}_{1}}{{g}_{2}}+{{f}_{1}}{{f}_{2}})={{c}_{1}}+{{c}_{2}}\] and \[{{g}_{1}}=\lambda ,\,{{f}_{1}}=3,\,{{c}_{1}}=1\] and \[{{g}_{2}}=2,\,{{f}_{2}}=1,\,{{c}_{2}}=0\] So, \[2\,(2\lambda +3)=1+0\Rightarrow 2\lambda +3=\frac{1}{2}\] \[\Rightarrow \lambda =\frac{-5}{4}\].
You need to login to perform this action.
You will be redirected in
3 sec
