(I just want to note that I made up this problem. I'm not trying to cheat on a test or anything.)
The point satisfies $\displaystyle \sqrt{(x-2)^2 + (y-1)^2} = 2$ and $\displaystyle y = 2x - 3$.
Substitution yields:
$\displaystyle \sqrt{(x-2)^2 + (2x - 4)^2} = 2$
$\displaystyle \sqrt{(x-2)^2 + 4(x-2)^2} = 2$
$\displaystyle 5(x-2)^2 = 4$
$\displaystyle (x-2)^2 = \frac{4}{5}$
$\displaystyle x-2 = \sqrt{\frac{4}{5}}$
$\displaystyle x = \sqrt{\frac{4}{5}} + 2$
Now you plug x back into the line equation to find y.
I just want to clarify that what I'm looking for is the point where that circle is intersecting the line. I'm not looking to solve for the X coordinate.
So I'm not looking for that answer that's around (4,5) I'm looking for the one that's around (2.9, 2.8)ish – I thought I would need pi.
If this is in fact the correct solution then I guess I need a little help figuring out what the 1's and 2's represent.