The orthocentre of triangle formed by the lines x+3 y=10 and 6 x^2+x y-y^2=0 is

Step-by-step solution

The given lines are x+3 y=10 and 6 x^2+x y-y^2=0 aligned & 6 x^2+3 x y-2 x y-y^2=0 & 3 x(2 x+y)-y(2 x+y)=0 & 3 x-y=0 & 2 x+y=0 & aligned On solving Eqs. (i) and (ii), we get x+3 (3 x)=10 aligned & 10 x & =10 & x & =1 aligned and array r 3 1-y=0 y=3 array Coordinates of B are (1,3) . On solving Eqs. (ii) and (iii), we get x=0, y=0 Coordinates of A are (0,0) . A line perpendicular to B C is 3 x-y= It passes through (0,0) , then 0-0= =0 The line A D is 3 x-y=0 A line perpendicular to A C is x-2 y= It passes through (1