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# Hyperbolas watch

1. Couldn't get anywhere with this question:

Q1. The tangent with equation ty=x+t^2 to the parabola y^2=4ax passes through the point (5, -6). Find the possible values of t, and the coordinates of the point of contact of this tangent with the parabola for each value of t.

Managed to start this one, but couldn;t get the correct y coordinate out:

Q2. Show that the tangents to the parabola with equation y^2=4ax at the points P(at^2,2at) and Q(as^2,2as) meet at point T(ats,a(t+s)). If PQ passes through the focus show that (a) st=-1 and (b) T lies on the directrix x=-a
2. 1) sub x=5 and y=-6 into eqn. of tnagent

-6t = 5 + t2
t2 + 6t +5 = 0
t=-1, -5

sub t-values back into eqn for tangent and re-arrange for x or y. Then equate with eqn of parabola and use b2-4ac = 0 if necessary.
3. 1) sub x=5 and y=-6 into eqn. of tnagent

-6t = 5 + t2
t2 + 6t +5 = 0
t=-1, -5
Man that's shocking, I need my basics brushed up.

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Updated: April 11, 2006
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