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)\"\" \"About 
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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( "\"abs%28PS%29%2Fabs%28PG%29+=+abs%28OS%29%2Fabs%28OP%29+\"\r
\n" ); document.write( "\n" ); document.write( "===> \r
\n" ); document.write( "\n" ); document.write( "===> \r
\n" ); document.write( "\n" ); document.write( "===> \"++abs%28hy-kx%29+%2Fd+=+sqrt%28x%5E2%2By%5E2%29\"\r
\n" ); document.write( "\n" ); document.write( "===> \"++abs%28hy-kx%29+=d%2Asqrt%28x%5E2%2By%5E2%29\"\r
\n" ); document.write( "\n" ); document.write( "<===> \"++abs%28hy-kx%29%5E2+=d%5E2%2A%28x%5E2%2By%5E2%29\", or equivalently,\r
\n" ); document.write( "\n" ); document.write( " \"++%28hy-kx%29%5E2+=d%5E2%2A%28x%5E2%2By%5E2%29\"\r
\n" ); document.write( "\n" ); document.write( "and this finishes the solution.
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