Need some help (1 Viewer)

[zeebobDD]

the question :
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 that 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) OP subtends a right angle at S
ii) PQ=PT

for some reason the proof of gradient multiplication isn't seeming to work:S can someone please help me thanks

 

[math man]

the problem with gradient multiplication here is that you want to prove angle OSP is 90 but if you use m1 x m2 = -1 it wont work here cause OS is a vertical line with infinite gradient, so you have to prove that PS has zero gradient. If you did everything right you should end up with p^2 = 1 so when you work out the gradient of PS it is 0 meaning angle OSP is 90. It is a very long process and i dont have the time to type it up, but i hope this helps

 

[zeebobDD]

my bad it should be QP subtends 90 at S but il try that way thanks for the help