the lones x-2y+6=0 and 2x-y-10+0 intersect at P.Without finding the coordinates of prove that the equation of the line through P and the origin of coordinates is perpendicular to 39x+33y-580=0.
First write the equation of line in the form of , now slope of the line is
Slope of line perpendicular to the above line is-
Equation of line passing through the origin and with slope equal to 11/13 is given by-
Substituting in , we get
Substituting in , we get
Since the point of intersection of lines , and is same. The line passes through P and origin is perpendicular to .