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 .

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