A) \[x-y=7\]
B) \[x+y=17\]
C) \[{{\left( x-12 \right)}^{2}}+{{\left( y-5 \right)}^{2}}={{13}^{2}}\]
D) \[{{\left( x-12 \right)}^{2}}+{{\left( y-5 \right)}^{2}}=2\times {{13}^{2}}\]
Correct Answer: A
Solution :
All three vertices lie on \[{{x}^{2}}+{{y}^{2}}=169={{13}^{2}}\] Hence, circumcircle of \[\Delta \] is \[O(0,\,0)\]. Centriod is \[G\left( \frac{12+13\,\sin \theta -13\cos \theta }{3},\frac{5-13\,\sin \theta +13\cos \theta }{3} \right)\] \[\Rightarrow \] H divides OG in 3 : 2 externally. \[H(12+13\,\sin \theta -13\,\cos \theta ,\,5-13\cos \theta +13\sin \theta )\] Whose locus is \[x-y=7\].You need to login to perform this action.
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