Conics Help PLEASE! (1 Viewer)

[adrenaline88]

Hey everyone,
Would really appreciate any help on the following questions (don't have answers for them sorry, my teacher got them from a 4u in-service or something):

To make it easier and reduce confusion, let E represent-
(x^2 / a^2) + (y^2/b^2) =1

1. P is a variable point on on E. The tangent at P meets the tangents at the extremities of the major axis at Q and Q'.
(a) If S is one of the foci, prove that SQ is perpedicular to SQ'.
(b) Deduce that, if S' is the other focus,
angle SQS' = angle SQ'S'

2. P is a point on E. The normal at P meets the major-axis at G.
(a) If S is a focus, prove that GS=eSP
(b) Deduce that, if S' is the other focus:
(S'G / GS) = (S'P/PS)

PLEASE PLEASE PLEASE help. My teacher has absolutely no idea what she's talking about- she's never taught 4u and actually had to study it during the holidays to teach us (pathetic I know ).

 

[turtle_2468]

Umm...
quick walkthrough for Q1: Let P be (x_1,y_1). Use tangent formulae (if you learnt them in class) to get Q, Q'. Now we know coords of S, so we can calculate the gradients of SQ and SQ' - let them be m_1, m_2. Now m_1*m_2=-1 hence they are perpendicular... if no one answers this by tomorrow I"ll make it more concrete