A hyperbolic line is a semicircle perpendicular to the real line.
You just have to find the two intersection points of the two circles and keep the point with positive imaginary part.
is a circle with center at (-1, 0) and radius and is a circle with center at (5, 0) and radius .
They are given by and . Subtracting one equation from the other gives a linear equation for x. After finding x, substitute back into either equation to get a quadratic equation for y. As Bruno J says, you want the point with positive y.