intersection points of line on a circle

[TOdorus]

Hi all,

I have a bit of an algebraic problem, and my lack of attention during math is starting to show. I was experimenting with hit detection based on lines for a simple shooting game, and the enemies bieng circulair.

I already have a function to check the distance from the line to the circles centre, so I already know that there is a intersection (or hit). I also would like to know where it intersects, for graphics and some extra physics.

So here's what I got:

Known:
r
m
b

so these can be considered constant

Equitions so far

y = mx+b
r^2 = y^2 + x^2

this gives:
r^2 = (mx+b)^2 + x^2

And then my troubles begin, because writing that out would give:
r^2 + b^2 = x^2 + mx^2 + 2mbx

Googling around tells me that this is the way to go, and you should get a quadratic function, but I don't know how to solve this kind of equation. Can anybody help out? I hope to finish a prototype soon.

Tnx in advance,

TO

[Exodar]

r^2 = (mx+b)^2 + x^2

And then my troubles begin, because writing that out would give:
r^2 + b^2 = x^2 + mx^2 + 2mbx

shouldn't you have the "b^2" over on the right side of the equation?
Like so,
r^2 = x^2 + mx^2 + 2mbx+ b^2

or alternatively,
r^2 - b^2 = x^2 + mx^2 + 2mbx

[TOdorus]

I noticed that too, this morning. I geuss it was kinda getting late.
I wanted it on the left side to have my known variables on one side.

[Exodar]

and did you get that equation solved? or do you still need some help with it?

[TOdorus]

I think so, but I haven't tried it yet. It's in another forum:

http://www.physicsforums.com/showthr...53#post1365553