2Q in L-transformation

I just a beginner for relativity (both GR & SR), so you find my question may be very simple but still hope you can help!!! THX~ :shy:

Q1. A light ray in the x'y'-plane arrives at the origin O' of the S' system at t'=0. it coms from a direction which makes an angle 30deg with O'x' and 60 deg with O'y'. Show that events on the front of the ray have coordinates is:

x' = - (sqrt3 / c)ct', y' = - 1/2 ct'
can I use the equation of transformation that x' = xo + ct' ? if yes how about the cos-function in fornt og ct'?

Q2. 2 events occur simultaneously at t=o in the reference frame S, at the origin and at the point (X,0,0). In the second frames S', the measured time-interval between the events is T. Prove that the distance beetween the points at which the events occur in S' is (X^2 + C^2T^2)

Am I right to use the space-time interval: (ds)^2= c^2(dt)^2+ (dx)^2? I have tried this method but the trem 1/[sqrt(1- v^2/c^2)] is left~~~ What's worng ??

yukyuk