The length of common chords of circles $x^2+y^2+px=0$ and $x^2+y^2+gy=0$ is
- $\frac {2pq}{\sqrt {p^2+q^2}}$
- $\frac {pq}{2\sqrt {p^2+q^2}}$
- $\frac {pq}{\sqrt {p^2+q^2}}$
- $\frac {2pq}{p^2+q^2}$
The common chord is the radical axis px - gy = 0. Its length is |pg|/sqrt(p^2 + g^2), matching option C when q in the options is interpreted as g.
Subtract the second equation from the first to get the common chord's equation as px - qy = 0, which is a straight line passing through the origin. The first circle x^2 + y^2 + px = 0 has its center at (-p/2, 0) and radius of p/2. The perpendicular distance from the center to the chord is found using the formula |p(-p/2) + 0| / sqrt(p^2 + q^2) = p^2 / (2*sqrt(p^2 + q^2)). Using the chord length formula 2*sqrt(R^2 - d^2), the length is 2*sqrt((p/2)^2 - (p^2 / (4*(p^2 + q^2)))). This simplifies to 2*sqrt((p^2*q^2) / (4*(p^2 + q^2))), which equals pq / sqrt(p^2 + q^2). The correct option is C.