Hey guys, I really need some help here. I would greatly appreciate some help and the answer which helps me most will receive Best Answer. Anyway, here comes the question now:

The point P(sqrt(2)t , sqrt(2)/t) is any point on the rectangular hyperbola C.
PART A.
Show that the gradient of the line OP is given by 1/t^2

Point Q on the line y = k - 2x where k>0 is a constant, is such that the distance OQ is as short as possible.
PART B
Given that Q is also on C, find the exact value of corresponding to Q.

PART C
Hence find the co-ordinates of Q and the value of k.

I can do (PART A) so don't worry about explaining that. But (PART B) is the real problem. The k in that line equation is driving me insane. I've tried doing all that I can do but can't seem to get rid of it. I'm confident I can do (PART C) if I can get the answer to (PART B).

I thank you all in advance.
Just so that you guys can check for yourself, the back of the book shows that the answer to Part B is t = sqrt2

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