The vertices of a triangle are \[[a{{t}_{1}}{{t}_{2}},\,a({{t}_{1}}+{{t}_{2}})],\,\]\[[a{{t}_{2}}{{t}_{3}},\,a({{t}_{2}}+{{t}_{3}})]\], \[[a{{t}_{3}}{{t}_{1}},\,a({{t}_{3}}+{{t}_{1}})]\], then the coordinates of its orthocentre are [IIT 1983]

\[[-a\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}}),\,a]\]

\[[a,\,a({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}})]\]

\[[-a,a\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}})]\]

The vertices of a triangle are \[[a{{t}_{1}}{{t}_{2}},\,a({{t}_{1}}+{{

1.	The vertices of a triangle are \[[a{{t}_{1}}{{t}_{2}},\,a({{t}_{1}}+{{t}_{2}})],\,\]\[[a{{t}_{2}}{{t}_{3}},\,a({{t}_{2}}+{{t}_{3}})]\], \[[a{{t}_{3}}{{t}_{1}},\,a({{t}_{3}}+{{t}_{1}})]\], then the coordinates of its orthocentre are [IIT 1983]
A.	\[[a,\,a({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}})]\]
B.	\[[-a,a\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}})]\]
C.	\[[-a\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}}),\,a]\]
D.	None of these
Answer» C. \[[-a\,({{t}_{1}}+{{t}_{2}}+{{t}_{3}}+{{t}_{1}}{{t}_{2}}{{t}_{3}}),\,a]\]

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The vertices of a triangle are \[[a{{t}_{1}}{{t}_{2}},\,a({{t}_{1}}+{{t}_{2}})],\,\]\[[a{{t}_{2}}{{t}_{3}},\,a({{t}_{2}}+{{t}_{3}})]\], \[[a{{t}_{3}}{{t}_{1}},\,a({{t}_{3}}+{{t}_{1}})]\], then the coordinates of its orthocentre are [IIT 1983]

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