Find chord length given equations for circle and line Is there any way to find the length of a chord if you are given the equations for the chord and the circle? Say you have a circle with an equation of $x^2 + y^2 = 4$ and the line $y = 3x - 4$. Is there any way to get the chord length from this?
I would assume this may be possible by substituting $3x-4$ for $y$ in the circle equation and solving for $x$ to get the $x$ values of the points of intersection, and then repeating this process but instead substituting $(y+4)/3$ for x, and solving for y to get the y values of these points. Then would it be possible to simply use the distance forumla to get the length of the chord?
Thanks in advance for any help.

Another way can be found to calculate the intersection points:
$$x^2+(3x-4)^2=4$$
For your work: We find
$$\left\{\left\{x\to \frac{1}{5} \left(6-\sqrt{6}\right),y\to \frac{1}{5} \left(-2-3
   \sqrt{6}\right)\right\},\left\{x\to \frac{1}{5} \left(6+\sqrt{6}\right),y\to \frac{3
   \sqrt{6}}{5}-\frac{2}{5}\right\}\right\}$$
