The centroid of the triangle formed by the pair of straight lines 12 x^2-20 x y+7 y^2=0 and the line 2 x-3 y+4=0 is :

Step-by-step solution

The separate equation of pair of straight lines of 12 x^2-20 x y+7 y^2=0 are (6 x-7 y)=0 and (2 x-y)=0 These the equation of sides are 6 x-7 y=0 (i) 2 x-y=0 (ii) and 2 x-3 y+4=0 (iii) On solving these equations, taking two at a time we get the vertices of a triangle which are A(0,0) ; B(1,2) and (7,6) Centroid of a triangle is ( 0+1+7 3 , 0+2+6 3 ) i.e., ( 8 3 , 8 3 )