A) \[\frac{1}{2}({{a}_{2}}^{2}+{{b}_{2}}^{2}-{{a}_{1}}^{2}-{{b}_{1}}^{2})\]
B) \[{{a}_{1}}^{2}+{{a}_{2}}^{2}+{{b}_{1}}^{2}-{{b}_{2}}^{2}\]
C) \[\frac{1}{2}({{a}_{1}}^{2}+{{a}_{2}}^{2}-{{b}_{1}}^{2}-{{b}_{2}}^{2})\]
D) \[\sqrt{{{a}_{1}}^{2}+{{b}_{2}}^{2}-{{a}_{2}}^{2}-{{b}_{2}}^{2}}\]
Correct Answer: A
Solution :
[a] The locus is \[{{(h-{{a}_{1}})}^{2}}+{{(k-{{b}_{1}})}^{2}}={{(h-{{a}_{2}})}^{2}}+{{(k-{{b}_{2}})}^{2}}\] \[\Rightarrow ({{a}_{1}}-{{a}_{2}})x+({{b}_{1}}-{{b}_{2}})y+\frac{1}{2}({{a}_{2}}^{2}+{{b}_{2}}^{2}-{{a}_{1}}^{2}-{{b}_{1}}^{2})=0\]\[\Rightarrow c=\frac{1}{2}({{a}_{2}}^{2}+{{b}_{2}}^{2}-{{a}_{1}}^{2}-{{b}^{2}}_{1})\]
You need to login to perform this action.
You will be redirected in
3 sec
