# Thread: Circle problem involving intersecting line.

1. ## Circle problem involving intersecting line.

Hi,

I'm struggling with a math problem involving circles:

This is the question:

find the coordinates of the points where the circle meets the line with the equations X + Y = 6.

I have already found the equation of the circle, the raidus and the centre of the circle. Here the are: Centre: (-1,2)
Equation of circle: x^2 + y^2 + 2x -4y = 8

I've tried solving it as a simulanteous equation and using the equation for the line and the equation of the circle but have been unable to come up with any answer. Any help is very much appreciated.

Thanks,

2. Hello,

I don't know if the equation is right.

Btw, x+y=6
That makes y=6-x

If you replace it in the equation of the circle (any point which is on both the circle and the line has coordinates that verify the two equations) :

$x^2+(6-x)^2+2x-4(6-x) = 8$

$2x^2+36-12x+2x-24+4x=8$

$2x^2-6x+12=8$

$x^2-3x+2=0$

$(x-1)(x-2)=0$

-> x=1 or x=2

---> {x=1 and y=5} or {x=2 and y=4}

3. Aaah! Thanks!

Substitute so the y terms are expressed in terms of x! I was trying (unsuccessfully) to subtract one equation from the other to 'get rid' of the ys or xs.

Thanks again (especially for the remarkably fast response)

4. You're welcome