Sorry folks, I'm pretty new to this and I do wrack my brain before I ask the question. I've exhausted all I know with this one.

The circle c had equation

x^2+y^2=17

L is the line

x-4y-17=0

L is a tangent to C at the point T.

Find the coordinates of T.

I can see that the line L is going to form a sort of hypotenuse radius within the circle.

I'm really struggling here and I am trying very hard which makes it doubley frustrating. I've tried to go down the quadratic route by stating x in terms of y with the equation of the circle but it turns into 4y^2+136y+289=17 and that's just way over the top for me. I'm pretty sure it doesn't factorise either so I've ruled that out, I think?

Any help greatly appreciated. I'm way off the mark here for an exam on Thursday but it has never really been in my power to make this on my own, hard as I've tried.