jee-main 2014 Q68

jee-main · India · 19apr Straight Lines & Coordinate Geometry Triangle Properties and Special Points

The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points $\left( a ^ { 2 } + 1 , a ^ { 2 } + 1 \right)$ and $( 2 a , - 2 a ) , a \neq 0$. Then for any $a$, the orthocentre of this triangle lies on the line
(1) $y - \left( a ^ { 2 } + 1 \right) x = 0$
(2) $y - 2 a x = 0$
(3) $y + x = 0$
(4) $( a - 1 ) ^ { 2 } x - ( a + 1 ) ^ { 2 } y = 0$

The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points $\left( a ^ { 2 } + 1 , a ^ { 2 } + 1 \right)$ and $( 2 a , - 2 a ) , a \neq 0$. Then for any $a$, the orthocentre of this triangle lies on the line\\
(1) $y - \left( a ^ { 2 } + 1 \right) x = 0$\\
(2) $y - 2 a x = 0$\\
(3) $y + x = 0$\\
(4) $( a - 1 ) ^ { 2 } x - ( a + 1 ) ^ { 2 } y = 0$

Paper Questions

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