The centroid of the triangle formed by the lines x+y=1 and 2y^2- xy-6x^2=0 is

Question

Accepted Answer

Correct answer: C. (c) Given that, the pair of lines 2y^2- xy-6x^2=0 ⇒2y^2-4 xy+3 xy-6x^2=0 ⇒2y (y-2x )+3x (y-2x )=0 ⇒ (y-2x ) (2y+3x )=0 ∴ Equations of sides of triangle are x+y=1, y-2x=0 ,2y+3x=0 On solving these equations, we get the vertices of triangle as ( 13 , 23 ) , (0 ,0 ) and (-2 ,3 ). ∴ Centroid= ( 13+0-23 , 23+0+33 )= ( -59 , 119 )

$The centroid of the triangle formed by the lines x + y = 1 and 2 y^{2} - xy - 6 x^{2} = 0 is$

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