Parametrics Q (1 Viewer)

[Stawt]

P is a point in the first quadrant of the co-ordinate plane, lying on the parabola x^2 = 4y. The normal to the parabola at P meets the parabola again at a point Q in the second quadrant. The tangents to the parabola at P and Q meet at a point T. If S is the focus of the parabola and if QS = 2PS, show that:
i. QP subtends a right angle at S;
ii. PQ = PT

Any help would be appreciated

 

[atBondi]

ok, well my first thoughts were:
find the eqn of normal, solve this simultaneously with parabola, to find q.
then use gradient formula with S( 0,1 ) ...
however the algebra in that is wayyyy messy... so im not quite sure..lol..
and funny thing is, were both 4 unit students and we cant do 3u maths...
how embarrassing..

 

[kcqn93]

i somehow got that.......



tricky question... or im just noob :\