If two sides of a triangle are given by 3 x^2-5 x y+2 y^2=0 and its orthocentre is (2,1) , then the equation of the third side of the triangle is

Step-by-step solution

Given pair equation of two sides of triangle, aligned 3 x^2-5 x y+2 y^2 & =0 (3 x-2 y)(x-y) & =0 aligned So, equation of sides are Perpendicular line to the Eq. (i) 2 x+3 y+k=0 which pass through the point (2,1) . 4+3+k=0 k=-7 Point of intersection of Eqs. (ii) and (iii) x= 7 5 , y= 7 5 ( 7 5 , 7 5 ) Perpendicular line to the Eq. (2) is array ll x+y+k=0 which pass through (2,1) & 2+1+k=0 & k=-3 array Point of intersection of Eqs. (iv) and (i) aligned x+y-3 & =0 3 x-2 y & =0 x= 6 5 , y= 9 5 ( 6 5 , 9 5 ) aligned So,