conics ques (1 Viewer)

[onebytwo]

Im having trouble with this question, it seems simple but i cant get it out.
AB and CD are perpendicular chords of the ellipse x^2/a^2 + y^2/b^2 = 1 and each passes through the same focus S. Prove that [1/(AS.SB)] + [1/(CS.SD)] is constant.
please dont do it for me, but show me the right steps to working it out.
Thanks

 

[Mountain.Dew]

Im having trouble with this question, it seems simple but i cant get it out.
AB and CD are perpendicular chords of the ellipse x^2/a^2 + y^2/b^2 = 1 and each passes through the same focus S. Prove that [1/(AS.SB)] + [1/(CS.SD)] is constant.
please dont do it for me, but show me the right steps to working it out.
Thanks

this is the rather long way of doing it, but it should work. please be advised not to use this method if other methods are quicker, more elegant and more efficient.

1) find the equation of both chords. use m as the gradient, and S as the point. note that the other chord's gradient is simply -1/m.

2) find the coordinates of the points A B C and D.

3) find the distances AS, SB, CS and SD using the perpendicular formula.

4) sub values into [1/(AS.SB)] + [1/(CS.SD)] and ur done!

 

[onebytwo]

cool, seems pretty simple
ill see if it works
thanks