document.write( "Question 1046270: The distance of a point P(h,k) from a pair of straight lines passing through origin is 'd' units. Show that the equation of the pair of lines is (xk - hy)^2=d^2(x^2+y^2). \n" ); document.write( "
Algebra.Com's Answer #662023 by robertb(5830)![]() ![]() You can put this solution on YOUR website! Let the origin be point O. \r \n" ); document.write( "\n" ); document.write( "Let the points R and S be where the line M perpendicular to line OP and passing through P intersect the two lines. (Note that line OP actually bisects the angle between the pair of lines.) \r \n" ); document.write( "\n" ); document.write( "Let the point S be (x,y), and let G be such that the segment PG is perpendicular to line OS.\r \n" ); document.write( "\n" ); document.write( "Then by similarity of triangles, \r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "===> \n" ); document.write( "\n" ); document.write( "===> \n" ); document.write( "\n" ); document.write( "===> \n" ); document.write( "\n" ); document.write( "===> \n" ); document.write( "\n" ); document.write( "<===> \n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "and this finishes the solution. \n" ); document.write( " |