Find Coordinates of point given length and formula of line

Okay, this is a coordinate geometry question I think. It is question 11 from IGCSE Additional Mathematics - October/November 2007 Paper 2.

This is part two of the question. In part one, I found the length of a line OB. It starts from the origin and goes until it meets point B. I have to find the coordinates of B. The formula of the line is y=2x and the length is 2√5. As I said before, it goes through the origin.

It is part of a right angled triangle BOA, with BA being the hypotenuse, OA being the second longest side and OB the shortest side. Length of OA is 3√5 and coordinate A is (6,-3). BO and AO meet to form the 90deg angle which makes it a right angled triangle.

Please help me figure this out. I have tried but cannot find a solution. I need to know in less than an hour

Thanks in advance.