SOLUTION: 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).
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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).
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let the origin be point O.
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.)
Let the point S be (x,y), and let G be such that the segment PG is perpendicular to line OS.
Then by similarity of triangles,
===>
===>
===>
===>
<===> , or equivalently,
and this finishes the solution.
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