Finding coordinates of a point on a circle( angle and distance from O known)

1. Oct 10, 2012

Wikeda

1. I basicly have to find the coordinates of P. All the pink lines are know, coordinates of points A and centre of circle are know.

2. (x-a)^2 + (y-b)^2 = r^2

3. I try to substitute mx+c into the equation and get

(x-a)^2 + (y-mx-c)^2 + r^2= 0

but I cant work out what m and c are. Any help would be appreciated! Am I in the right direction, or am I completely off?

2. Oct 10, 2012

Mentallic

I'm just going off what it looks like on the picture, but it looks as though P is the intersection between a line with gradient -1 going through the centre of the circle and the circle itself. Is this correct?

If so, what is the equation of a line with gradient m that goes through the point (a,b) ?

EDIT: And by the way, if you were trying to find where a general circle intersects with a general line, then you need to plug
$$y=mx+c$$ into the equation
$$(x-a)^2+(y-b)^2=r^2$$
to get
$$(x-a)^2+(mx+c-b)^2=r^2$$
And then you'll have an equation that you have a quadratic in x that you have to solve (all the other values are constants, so the answer will depend on what those are).
Once you've done that, you can plug that value of x back into the line equation to find y (you can also plug into the circle equation but it's harder work to solve for y there and you also get two values).

3. Oct 10, 2012