The length of the common chord of the circles ${\left(x-a\right)}^2+y^2=c^2$ and $x^2+{\left(y-b\right)}^2=c^2$ is

If $\alpha , \beta$ are the roots of the equation $35x^2-24x-35=0,$ then the parametric equations $x=\alpha +a\cos \theta , y=\beta +a\sin \theta$ can represent a family of

($a$ is arbitrary constant)